Yikes. I agree that, regardless of the child's behaviour, this does not sound like a good working relationship with the parents!! I would not accept that kind of response if I told a parent that their little person SPIT on someone.
I think I would decide what the "non-negotiables" are. Like zen39 said, pick your battles. I would not worry about her not wanting to talk to you or other people on demand, unless you are trying to get a response that you need immediately. If she doesn't want to be comforted, then just remind her that you are there if she needs you and leave her to her own company. If she is being hurtful to you ("I don't like you/ being here") then remind her to use kind words, and then let it go. If you are insisting on manners, as you should, then begin letting her know that if she doesn't use them properly, she may not be allowed certain things. Some of the things that I would make issue of, not ignore: locking the bathroom door (safety issue!!), spitting/hitting etc or being downright disrespectful, being hurtful to the other children (with her words), any kind of aggression.
She is obviously having a hard time with her brother being gone, because it seems like mom and dad use him as a third parent, so to speak. It's great to be helpful as an older sibling, but this is they kind of situation that it turns negative. Now that he is at school, you have an opportunity to allow her to be more independent. And she will learn, eventually, that if he is not here to do it for her, she'll have to be the one that does it.