How to keep the peace without losing my MF mind.

So back story i have had a child with a very bad man and thats putting it politely. Violence in the past and did a Claire’s law check and its worrying. Now i know this word gets thrown around alot but he has every characteristic of a really bad Narc. Ill keep this as short as possible. He hasn’t been in my child’s life ignored them for like the first 2 months of their life so wasn’t around for birth certificate. Has never paid a single penny. Then has been in and out messed up most visits either late picking up, dropping off just simply not turning up. Has said doesn’t care about our child said they are just mine just been on the whole nasty. Then he has claimed the reason he doesn’t see our child is because i wont let him because he wont take my eldest child who he treated like his own child until i got pregnant which i have never i just said they will be pretty upset if they don’t go with their sibling so could he have a think. Then he said he can’t do visits because he wants a DNA which i tried to organise 3x times and he ignored all the messages. Then he said he’s not doing visits because he’s not on the birth certificate and he wants me to pay to add him to it. 🤦🏾‍♀️ I obviously said no because he had his chance (6weeks) he didn’t come, then has been horrid. So now his mum is saying she’ll pay and she wants his name on the birth certificate shes been using the standard manipulative tactics i can spot a mile off guilt tripping, playing the victim, blame shifting. Then telling me i will get the silent treatment if i don’t do it. I want my daughter to still be in contact with dad’s side of the family. Most of them are ok. So now i feel backed into a corner if do it he goes on and now legally he can fuck me about on visits probably keep her longer then hours discussed and know i can’t do anything. And i don’t have funds to go court And he will purposely ignore the other child. But I don’t want my child when older to think im the bad guy when all im doing is trying to do is protect everyone from further heartache. At the minute we are all left alone and have peace ☮️