yes, you can use a banishing spell to send someone away, though i'm not sure how effective such a thing is. the energy would make the person uncomfortable and want to leave, but if this is someone's partner i'd suggest also doing a break-up spell. in your efforts to send one away, you might have the two of them move. once the person is gone, a protection spell is a good idea, but this is more to protect from energies.
of course, depending on the situation, you can always call the cops if it's a criminal offense.