Have you had a chat about hormones, and that while it is difficult to control your outbursts (both yours and hers), it still isn't acceptable behaviour and needs an apology when things are calm?

With teens, I find that you need a calm, rational head and an ability to see yourself through their eyes: both when you say things that are inadvertantly hilarious to them, and when they cannot understand the system and consider it unfair. That is not to say you must change your policies, just be able to see where your teen is coming from. Maybe your OH needs to step up right now as he will be in a more rational headspace, while you model acceptable hormone fallout damage limitation? (FWIW, backchat is often an attempt at negotion with no diplomacy skills.)

As for listening - what is she doing when you are talking? Ensure you have full attention before asking her to do something, turning off the TV and standing in front of her if you have to. Same as with a disobedient toddler, or a frustrating OH. It is the same principle: they have something they want to do, so it's hard to tune in and concentrate on the person trying to get you to stop having fun and do something you don't want to do.

HTH.