I think this means that, right now, you're on a warrior path. You have the means to stand your ground. You might not have so much power yet that any attacks won't leave you devastated, I mean you're getting attacked at all, so parts of you are going to be sacrificed as well as ideals that you hold dear, represented by the deaths of your family members. Your grandmother and your sister remain, representing the surviving sort of feminine aspects of the path.
The angelic weapon represents the masculine aspect of the path to which you're called and the demonic opponent I think highlights that polarity. Since I'm an alchemist, the language that I use for this process is separation, which tends to be very martial.
Some of this sounds eerily similar to my own dreams while I was on the warrior path (and might still be on, a little bit). Severing the head was one, representing a call to maybe not think about it too much and connect more with your instincts--as you mention you did a little, and that's served you well. My beheaded opponent was a shapeshifting giant in the form of a lizard, and in the dream I had to bring the severed head to a grandmotherly witch who lived in the woods beyond this field of dragon gates. That's what represented my return to instinct--and the presence of the women who watch the warriors, which is a spiritual archetype present in a number of traditions: disir, valkyries, fates, I even consider the banshee as a vilified form of what might have once been a benevolent warrior-guardian granny.
Eventually, I got stuck with a weapon that was entirely wrong for my build, too. It's a reflection of the spirit, not our physicality or our skill. Swords in particular are a masculine symbol with masculine notion, and that's what opened me up to working with my Animus (which also comes to me as a sort of spirit guide, but whether or not you've got one or will meet one isn't something I can say, because this is your path.)
The transformative process of "death" is something we both take and dish out in little ways, many times before it happens in a big way.
Each dream could signal a progression along an "inner alchemical" reaction, which of course I'd say because I'm a Jung-influenced alchemist. Basically, it's training or practice. It could also be that you have the warrior skill somewhere in there, second nature from a past life, and if something beyond the corner of your eye starts to get nasty then you can just...handle it. Once every three months, ethereal pest control! That's just the way it goes, sometimes, when you notice this otherworld.