warning: long wall of text coming

My fiance has a daughter from a previous relationship, let's call her E. They were not been very 'close' because she lived with her mom in another state. When E was 14, her mother relinquished her parental rights but E didnt want to move here, so she moved with her grandmother (my MIL). Two years ago, E finished high school and she decided to move in with us so she could go to college here in the city.

Six months living here, fiance and E started constant fights about teenage behaviour: rude, inconsiderate, disrespectful. I understand it's normal but the bad attitude has been escalating. I never try to act like her mom because I'm not but I constantly try to give her emotional support though she rarely accepts my help. The rules here are very clear and we have spoken with her a million times about unacceptable behaviour and she had been warned that the constant escalating 'will result in her not being welcome here anymore'.

This happened last week:

Friday, fiance called E at 11:30 pm because she knows she needs to ask for permission before going out with friends, especially if she will be out until late or staying over at a friend's house. He sent her a message asking her whereabouts and so. She just said 'We'll talk tomorrow' then stopped responding. This was not the first time but other times she would apologize and recognize she did wrong. When she came back saturday morning fiance started saying that what she did was wrong but she started to blame everything on us (?). That day she continously disrespected both me and my fiance with plain rude remarks. 

Sunday: discussion regarding an important document she lost escalated quickly to her telling fiance to 'fuck off' and screaming, to which he (wrongly) reacted screaming louder and throwing her out of the house (she is not a minor). I calmly asked her to leave because fiance was (wrongly) acting crazy and told her to "stay with her boyfriend, where she had been staying when she didnt come home" and she left. My intention was making her stop a growing conflict, a crazy situation.

I was aware she was not 'staying in the street'. She did go to her bf's house but it seems wednesday she drove 2 hours to nearest relative's house at midnight, next day she called demanding child support. Saturday  they made up when she asked to come back home. 

Fiance and I spoke and I told him I was worried about this toxic environment and the fact that their discussions were dragging me into constant anxiety. I told him that he was the main asshole, but that's another story.

E is back home, she apologized to her dad (and he apologized too) but I have not spoken to her because I work funny hours so I haven't seen her. We seriously discussed asking her to live somewhere else, give her child support so she can pay for a room to stay near her university

AITA for feeling relieved if this happens?