Should a 5yr old choose which parent to live with?

I have twin sons with my ex. We share custody. Since our breakup and him falling in with a woman old enough to be his mother, things between us has been bad. Recently we’ve gotten into arguments about who is allowed to do exchanges. Well sometimes I need to have other people do it for me as I’m busy with one thing or another. Since I sent someone he didn’t want to do exchanges with, he called me complaining and I just basically told him I didn’t have time for it and hung up. The next morning he had the nerve to call my mother! He’s telling her that his gf/wife/whatever never started anything with me because apparently she knows he’s not going anywhere and that I’m just mad. Well idc. I’m not doing exchanges with that bish no matter what anyone says even if they are married. He also tells her I’m the one causing the problems. Excuse me but he left when I wasn’t even 6 months pregnant, I think that’s what caused our problems. My Mom confronted him about the fact that the boys treat us differently than they treat his family. It’s like they never want to be here; when they’re here they always talk about whatever happened over there and to make matters worse, the last time I did the exchange, one of them said he wants to live with his dad and come to my house on the weekend! He’s five years old! How can he possibly know what he wants? Someone from over there his telling him to say this bullshit. Like they’re trying to take my kids and make my life more difficult. My mother confronted him about this and of course he denied it all. I feel like my kids are being turned against me and he’s calling my mother to turn her against me too. I’ve tried to get him to let me just move to another state but he refuses. He’s gonna say that I can go but I can’t take the boys. Well if I can’t take my boys, what’s the point? It just feels like EVERYTHING in my life is falling apart.

Edit: I’m not jealous. I’m half her age and have nothing to be jealous of. She doesn’t mind that he uses her for her money and to drive her cars and to live in her house rent free. I definitely don’t want a man back that would leave a woman when she’s pregnant with TWO of his kids. It’s not like he dumped me. I actually broke up with him first, because he wasn’t fulfilling his promises. Eventually we would’ve gotten back together but he let her come between us so no I don’t want a man that would walk away from his family.