Maybe I'm the odd one out of the bunch (maybe because I'm probably older than the typical ATOTer)
1) You knew she needed a place to live. If she had money, she would have just got her own apartment. So you knew she had nothing to give you. You let her move in anyways.
2) You knew she had a kid, with no father figure. Its likely you'd have to play temporary dad and have kids ****** in your way. Again. You let her move in anyways.
3) You knew she had a cat. You knew its going to claw things, piss on everything, as that's what animals do. Again. You let her move in anyways.
4) You knwe she had no car... You knew she'd probably have to borrow yours. Again. You let her move in anyways.
See a pattern?
The only person you have to blame is yourself! Instead of being a man, and accepting that fact, you decide to want to control this gal instead. Sure, maybe not aggressively, but in a passive aggressive way. "You owe me because I did this and I'm inconvienced and you offer me nothing." Thats not how friends interact with each other.
I can see why she is pissed. When you live in a place with friends, you both have to make compromises, and respect each other. To me it sounds like you told your friend that she has a room, and she has to live out of that room. If it was 2am and your friends were over smoking and she came charging out of her room. Apparently she was sleeping and looking out for the welfare of her child... Wouldn't you do the same thing in her place? Did you respect her or her kid? Apparently not... Then having your friends start ****** with her when she gets pissed. I'd be pissed too if I were her!
Grow up. Don't use the excuse "she paid me nothing..." You offered her a room in your place with no lease, no expectation of money, or anything else... You can't use that against her and use it as an excuse to disrespect her or her kid... If you don't like the arrangement, cancel it. Tell her that you feel restricted with her there, and her temporary stay is at an end, and she has 30 days to move out... But you still have to respect her until she moves out.