12 yr old daughter wants to live with mom because of dads girlfriend?

I'm about to lose my mind ,NO Really! I'll try to make it short. I have primary residence of our daughter Her mom came to pick her up from school about six months ago claiming that my daughter was miserable due to my girlfriend. Daughter and girlfriend at times didn't see eye to eye but nothing horrible. Girlfriend has 2 boys and we all got along fine, me and the girlfriend had occasional fights sometimes curse words involved. My daughter seems to hate my girlfriend now even more than ever i know her mom has alot to do with this because she talks SO much crap in front of my daughter. My daughter doesn't even want to come to my house to visit. My ex cannot stand the ground my girlfriend walks on and she lets everyone know. She's even went as far as trying to get a restraining order on her on behalf of my daughter. She is literally making my life a Living hell and don't know how much more i can take. My maine concern is my daughter and THATS IT. I could easily go pick her up and make her live with me but that would devastate her. I have asked her what if daddy gets his own place, would you then live with me. She says ( i will visit you and and spend summers and vacations but i want to try living with mommy). The worst part is since her mom got her she constantly threatens me with child support and wants me to pay this and that and calls me a poor excuse for a father because i stayed with my girlfriend. I have raised her on my own since 06 and got a girlfriend a couple years ago. I'm at the point of seriously evaluating if it is worth staying with my girlfriend and just giving up custody. She wants her mom anyways why would i fight for my daughter if i'm just gonna end up having her hate me for not letting her live with her mom. My girlfriend tells me to just go pick her up (she's a kid she'll get over it). But she's not the one that sees her kid cry and hurt for her mom. My daughter is my world and at times i have SO much resentment towards my girlfriend for driving a wedge between us. I'm so confused on what to do