I know every teen is different and the mood swings, I think, are just a part of that age group. But they need to control their responses to you. We would never allow them to give us looks or slam doors. If it happened, each and every time we called them on it--which takes a lot of energy and dedication :-)
If my child slammed a door, I would tell her one more time and the door will be taken off and put in the garage. Don't just say it, mean it and follow through. Earphones in the ears while you are trying to talk to her, then take them away. They have to understand the you are the parent and deserve respect.
If trouble started with one of our girls, we sat down and I told them - we don't treat you like that and we can't allow you to treat us like that. We made a real effort to keep things "up." I would ask her why she is frustrated with you and let her know it is hurtful and can't be allowed.
I really believe that ignoring it is not the answer, and that they can control it. They don't act that way with all people so that means it can be curbed if they want it to.
Good luck - these are hard years, I remember very clearly.