How should I handle this?

I'm really over having to deal with my child's father and our son is only 3 weeks old. We broke up a week before he was born because he cheated on me.

Currently he comes over to my house and spends time with the baby for a while and then leaves sometimes he spends the night which i agreed to at first because he wanted to be able to help me in the middle of the night....but he doesn't. PLUS he claims he still wants to work on things with me but still will text other women right in front of me lol .

I just want a situation where i don't have to see him as much. Here's the issue.

Initially I thought he could take baby to his house for a couple of hours a day but he thought of being away from my baby and not knowing what's going on makes me emotional. Not to mention it would be his moms house and there tends to be lots of kids there and she has a small dog and I don't want my baby to get sick etc...

How should I handle this?