Am I giving him too many chances?

My dad is super toxic. To show a few examples, he references deceased family members during arguments, fakes medical conditions for attention, and has even threatened to falsify a rape report on my babies’ dad to get get his way in an argument and thought it was funny. He hated my babies’ dad up until we had our first, then acted like nothing happened, talked/acted like he was a “new man”, and was insisting that my babies’ dad moved in with us. We tried for a little while and it didn’t work out, so we moved out.

That was probably about 6 months ago and I’m also now 7 months pregnant. Since then, my dad has tried to bribe me into moving back, promising things that I know are not realistic, like quitting addiction - claiming he would do it “only for my son because he loves him so much”, a car and insurance I know he can’t afford, etc. So I just kind of ignored it and we visited as often as we could, probably 2-3 times a week.

Almost a month ago, he texted me and lied saying my mom told him she was suicidal because she blamed herself for me moving out so I needed to move back urgently. My mom said this wasn’t true and a sibling who overheard the convo also said it wasn’t true.

I cut him off for a little bit but then he kept making efforts to talk again. And I was going through scares with baby #2 and thought I could use all the support anyways. But then tonight, we were texting and everything was fine but then he started up. He said “it breaks my heart I don’t get to see you guys as much as when you lived here”. Thinking he was just genuinely sad, I apologized and said that we could make even more special plans so he feels more involved. He seemed okay with it and we carried on for a little bit but then he started sending me picture of my son as a really little baby and I was saying how cute they were and he said “imagine if he just disappeared and had a kid on his own, like you’re doing to me” and started saying again how my son is so special to him that he would quit drinking for him, only if we move back.

My mom says I should stop responding to him, at least for a while, to see if it will get him to realize that he needs to relax a little. My babies’ dad says I am being too nice to him after all he’s done and shouldn’t have access to our babies and shouldn’t have any more chances.