Ausar isn't exactly a netjer of the Duat, he is more so a netjer of the dead. The reason for this distinction is that he is a dead god, not a living one like Inepw (Anubis). He is a dead man, one who has lost his life. In returning to life, he could never again dwell with the living. Yes, that is unfortunate, but it is necessary, and Ausar knows it. This detail is so very important and necessary to the story; he knew it was in his nature to die.
You left out so many important details of the story, I am honestly a bit appalled. It scares me slightly that someone so interested in my path, hasn't researched it a bit further than the most basic of things. I will include a fuller version of the myth at the end.
Yes, your ordering is correct, however, Geb and Nut had a problem, as Re became jealous of the love that the two felt. He also didn't want their love to prevent him from continuing to create. However, his biggest issue was that Re heard a prophecy that one of Nut's children would one day overrule him. In another myth, he is also her lover, and doesn't want his indiscretion shown. However, due to one or several of these reasons, Re forbids that Nut give birth on any day of the year. During this time, the year was 360 days long, not 365. Djehuti, in either his love for Nut, or his wish to put her out of pain, gambles with Khonsu, the netjer of the moon. He hustled Khonsu, and the last bet being for 1/16 of his light each day. This adds 5 days to the calendar.
These five days were unlucky, and occurred right at the end of the Kemetic year. Please note: five days. Each day, a netjer was born. First, Ausar or Osiris, then Set, then Auset or Isis, Nebthet or Nephtys, and finally Heru or Horus. Yes, a Heru was born with the others. He is Heruwer or Horus the Elder.
Heruwer is the brother of Set who is ever locked in combat with him as equals. Neither is defeated and neither defeats. They are night and day, Deshret and Kemet, life and death. They are balanced, and yes, this version is older than that of Herunadjitef or Horus, savior of his father.
Ausar's relationship with Set was interesting, as Set was actually his coruler. Set controlled a portion of Kemet under the authority of Ausar. So yes, Set did have a good claim to his throne later when he fights his nephew and brother.
Not only this, but Set was a netjer full of life; he was active, he was violent, he was lustful, he was taking of the pleasures life can give. Ausar, on the other hand, was passive, he was relaxed, laid back, he took his time. Ausar was death before he was dead, he had never laid with his wife; Set had 5 during his lifetime, and a tryst with Heru (I promise, I will explain.) Set is not death, though he could be said to be jealous, he wanted to be the first born son so badly, he burst from his mother's side, rather than wait his turn. He wanted the good things in life, and thought they were his to take.
And yes, in a sense, they were. If Ausar could not defeat him and easily, he was not worthy of the position, as some of the former netjer Nisutbity were not. When a Nisutbity becomes weak, they can no longer protect Kemet, and have no place in the position. So, yes, Set had the right to challenge his brother, and even to kill him. I will not defend how he did it, but I do not agree with it being pure jealousy. I think Ausar's very nature offended him, and at one point, Set defends his actions by saying he had been offended. Set gave him the death he so craved in his very being.
Ausar had to die, for many reasons. Before Ausar, those who died had no true place to go, no home to reside, and no friendly netjer. Yes, there were netjeru of the Duat, but they weren't dead, they couldn't remain in a place reserved for the dead. By Ausar dying, he gives us a home, he saves us, he gives us a friend, and most importantly, he gives us an afterlife.
Before Ausar, yes, things were mummified; snakes who assisted in creation to be exact. But these beings were and are dead, and only will revive once the world comes to a close. The Creator mummified them for their assistance in creating the world. These snakes died, because they were a part of the Nun and the uncreated world. But there was no afterlife for anyone, not even those snakes. They, like us without Ausar, are trapped within their khats or physical bodies forever. Ausar, through his death and rebirth, gives us a death and rebirth. He gives us a way to return to life and not be in a hellish eternity.
So no, please, don't place blame on Set. He was only doing what was necessary, whether he knew it or not.
The most commonly known form of this legend comes done to us from Plutarch, and so may or may not be entirely true to the Kemetics, however there is historical evidence that shows it to be at least partially true. I have added other details in of different ways it has been foretold in the attempt to be as through as possible.
Ausar, rules over Egypt as a goodly king, bringing many blessings to the world because of this; agriculture and civilization included. Set places himself here as the jealous brother, who due to not being born first, will not ever hold the crown of Egypt. Regardless, Set is jealous of what his brother has; the throne, the love of the people, the support and love of the other netjeru. He sees his brother has all these things, and it angers him, it makes him want to take it all from his brother and claim it for his own.
It's a bit weird for a reference, but it kind of reminds me of the Loki from the Avengers comic books and the movie. He is so consumed with what he doesn't have, that he doesn't see what he does have.
Set begins to plot against his older brother, deciding that since Ausar has no heir, he needs only to kill his brother, not only removing him from rule over Egypt, but also showing him to be a weaker man, and so allowing Set to take Ausar's place. So, he threw a very very lavish party, inviting everyone. Ausar, even though he is warned against it by Auset (Isis). At this party, Set comes out with an even more lavish chest/box. He offers the chest to any netjeru who can fit perfectly within the chest. Unknowingly to all, he had Ausar measured, so that the chest would fit his body perfectly. Everyone tried, until it came around to Ausar's turn. In this moment, Set pounced upon his brother, slamming shut the lid and nailing it closed and pouring lead over it to ensure it would stay closed. He then threw the chest containing his brother into the Nile, and it floated away.
Auset begins mourning for her dead husband, and begins a search for the chest containing his body, so that funeral rites can be done so Ausar can rest. She asked everyone she met, until a group of children eventually told her that they saw Set throw the chest into the mouth of the Nile. She begins enquiring of lesser spirits of where her husband's body cameto be, and eventually landed in Byblos, where it connected with a small sapling. This sapling grew up very fast, becoming of an amazing height and thickness. The king of Byblos came upon this huge tree, and had it cut down, and the trunk made into the central pillar for his palace. Auset went straight to this palace,and,speaking only to the queen's maidens, she treated them kindly, braiding their hair and breathing fragnant breath upon them. When they returned to their queen, she questioned them about their hair and perfume, and so it came about that Auset became a nurse to one of the princes.
She fed the boy by allowing him to suck on her finger, and every night she placed him in a fire, while she turned into a kite and lamented her fate. News of this reached the queen, and so she hid herself and watched this one night. The queen rushed to save her child, and by doing so, lost immortality for him. Auset then reveals her fate and her purpose to the queen, begging that the pillar be cut down and given to her. She was given the chest, and returned to Egypt with it.
When she returns, she mourns her husband, and Set comes upon her mourning. When his sister lays down to sleep, he took Ausar's body, and cut it up into 14 pieces, then scattered them throughout Egypt. Auset, realized what had happened, and then went in search of the 14 pieces. Thispart of the myth diverges two ways, the first is that she embalms, mourns, and buries each piece separately, erecting a temple each place that she finds and buries the piece. In this half of the myth, her child, Horus the Child or Horus the Son of Isis is already born. The other half, is the more important to the cult of Ausar.
She, sometimes alone and at other times with her sister and Set's wife Nephthys, finds and gathers each piece, until they have found 13 pieces. The only piece they did not find was that of Ausar's penis, which had been swallowed by a fish that was then thought of as sacred, and which was not to be eaten. In order to ensure he is whole, she creates for him a phallius made of clay, and embues it with magic so that it works just like the real thing. (For the Kemetics, the penis was not only the seat of sexual power, but that of power in general. For Ausar to be left without his phallius would leave him in a weakened and incomplete state forever.) Together with Ienpw (Anubis), Nephthys, and Djehuti (Thoth), she embalms, mourns, and brings her husband back to life. Once Ausar has been returned to life, she turns herself into a kite, flies over Ausar's phallius, and becomes impregnated by him.
From here, Ausar's myth then carries over into Heru's myth.
Auset, pregnant with little Heru, takes off to hide herself in a swamp marsh. In her going, she takes seven scorpions to protect her on the road and after, and they cause her many problems with their overprotective actions.
Little Heru is bitten by many nasty things and nearly dies several times, always with his mother saving him at the last moment (mom is working hard to provide for him and can't stay home constantly). After a hard childhood, he grows up strong enough to fight his uncle.
Skip forward 80 years into this conflict between Heru and Set, with Set calling Heru a youth who is arrogant, and Heru calling Set an old murderer. After several fights and issues Re gets fed up, and tells them to make nice at Set's place. Later that night, as the two are laying in bed, Set attempts to rape Heru, only Heru puts his hands between his cheeks and catches the semen. Heru runs home, shows Auset, and she cuts off his hands to rid him of Set's claim. She then gives him new hands and has Heru use a jar to contain some semen. They go to Set's garden, and after asking the gardener what Set likes best, sprinkles it on lettuce. Set comes along later, eats some lettuce, then heads off to the tribunal. Set says he raped Heru, and as such has a claim to the throne. The tribunal boos and spits at Heru, telling him he is not worthy of the throne of Kemet. Heru makes the same claim, and Set gets the same treatment. Djehuti calls up both of their semen, while Set's answers from the river, Heru's answers from inside Set. Djehuti asks that the semen come out, and the semen answers "From where shall I come?" Djehuti says, "Come out his ear!" "I can't come out his ear, I am divine semen!" "Well, then come out his head!" The semen appears on his brow, and Set attempts to rip it off and destroy it. Djehuti snatches it away and places it upon his own brow as the moon.
After this, their conflict is resolved. Yes, it is longer than I made it sound. I just thought I might give some sort of break on this.
Set represents chaos, Heru represents order. Through Heru's control of Set, he is putting chaos on a certain level, one that can be controlled towards a good result for all involved. However, Set should be honored as much as any of the others, as he was for the much of ancient Kemet. Most of the hatred for him came after foreign invaders took over Kemet and adopted Set as he is similar to Ba'al. He was a netjer given a bad reputation, and not for anything he should have been for.
He protected Kemet from weak rulers, he gave us an afterlife by sacrificing his own reputation and property, he has done much. Though I fully admit to my bias for him. :)