Thank you for the additional information.
You are certainly in a hard place.
It sounds like you really have gone out of your way to build a relationship with your stepdaughter but she has never really reciprocated. Her dislike of you does not seem to be towards who you are, but more towards the situation (she likely didn't want her father getting married to anyone and it's possible that her biological mother paints a poor picture of you at home).
To address the situation you described about the pre-prom party I would recommend that you speak with your husband and ask him to drop in the fact that in order to organize the party she will need to coordinate with you. In fact by giving in to this situation of her not talking to you and disliking you openly your husband is doing his daughter a big disfavor. He is indirectly teaching her that it is ok to hate somebody for no apparent reason, be disrespectful towards them all while spending time at their house (the house is not just your husbands). This lesson will no doubt create problems for her later on. Instead she should be taught that should she have an issue or problem with somebody she needs to come forward and discuss it and agree to a set of solutions. Unfortunately, at this point she is only being encouraged in developing a sense of entitlement where it is ok to do as she pleases. For this reason it is very important that you speak to your husband and have him change his approach.
Something your husband can do going forward is defer decisions to you. This will indirectly and subtle tell her that she cannot possibly spend time at your home without communicating with you. So for example if they ask to go to the movies or lunch or a theme park etc. on their day with you guys, then your husband can defer the decision to you and say that they need to check with you and get your buy-in. In this way he needs to facilitate interaction and should she behave inappropriately he needs to intervene and lay out ground rules.
If he is unable to do this - you can think about laying out certain ground rules yourself. Such as if she is rude and does not answer you when you speak with her there will be no TV allowed on her day spent with you etc. Or she won't be allowed treats or privileges that her brother will be allowed. In other words teach her that there are consequences and her rude and irrational behavior will not be accepted by you in your house. I would recommend first speaking to your husband and having him facilitate interactions before adopting this more hard lined approach.
I hope this was helpful.
Please do let me know if you have additional questions/thoughts.