Co-parenting with an ex

Hey y’all.. here to vent and get some suggestions on how to co-parent with an ex. So lately, my baby daddy has been sleeping over to take care of the baby. I feel like he doesn’t put in effort or love into our little girl because she will non-stop crying when he holds her. So I supervise for that reason (and other reasons, let just say he get impatient easily) so I don’t feel comfortable with him handling her alone. The reason why he sleeps over is so he can prove to me that he can take care of her through the night because eventually he wants her to sleep over at his house, which btw she is one month old. It just seems wrong for him to have her at this age… So now I want to stop these sleepovers because it just ends up in me loosing more sleep and having to take care of two babies Anyways I just want to know how the fuck do I co-parent with him cause truly deep down I don’t want to be with him. He is aggressive, rude towards my family, doesn’t interact with my family and these are important qualities for me in my partner… also he says he wants to change but trust has been broken so many times with saying he wants to change but eventually shows me that he doesn’t. Also I’m low key worried about how he will react if there are more restrictions- he also finds a way to wiggle his way back into my life… he feel bad for him at times when he says he feels lonely… so I take him back…