sounds like shes pretty upset with you about something.
I would try to be nice and treat her good but when shes out of line very matter of factly and with little emotion explain what she did and dole out the punishment. I wouldnt allow her to get a read on how you feel it sounds like she will play that to her advantage if she can. I'd also treat her well and try to encourage healthy dialog with her when shes not in trouble etc even tho you might still be frustrated with her about this or that.
almost souns like she feels the need to get back at you for osmething. Shes entirely entitled to feel mad at you all she wnats but she still needs to behave and respect her parents etc..
I hope she comes around. those teen years can be killer with kids too. I"m lucky with my kids but i've seen some 13 year old girls wow they got some mouths on them lol!