Ex taking me to court for baby he never cared for England

2 months ago I left my 6 year relationship and took our 8 month old EBF daughter with me. There is a long history of narcissistic and physical abuse from him particularly when drunk. I was advised to leave him off the birth certificate by a social worker and the registrar after he hit me in the stomach after my emergency c section and needed checking out at A&E. He frequently walked out of the family home and disappeared with no contact for a week at a time before coming back. The last occasion was an argument about sleep deprivation and me begging and crying for more sleep. He was continuously waking me up asking when she was last fed asking where her nappies were etc after agreeing to let me sleep. There have been times where I’ve had complete meltdowns screaming and crying and he’s recorded these after deliberately provoking. He has seen her a handful of times since I left and I have updated him on all her progress. He didn’t show up to her medical appointments for issues she’s had since a complicated birth via emergency c section. He hasn’t really asked anything about her off his own back either only if I mention it. He hasn’t bought her anything clothes toys etc. These visits have all ended with him being aggressive about adding him to the birth certificate and shouting in front of the baby. I did suggest he makes genuine effort with therapy and stopping drinking and we could revisit the conversation in 3-6 months. This angered him even more and he has since been to a solicitor and sent me a letter requesting an updated birth certificate and contact with her including overnights. I have seen him in person once in public since this letter where he threatened that he will take me all the way to court as his parents have all the money in the world. He is now moving back to his family 4 hours away and insists he will drive up every weekend to see her and that I must cooperate with this. Does him moving away affect his argument? His parents are very wealthy and his mother has always bullied me including demanding I had an elective c section so they could plan a holiday, saying the news of the pregnancy ruined their marriage among hundreds of occasions of belittling me and generally picking on me because I don’t come from money. She also refused to hold the baby in the hospital. His parents have met her twice as they insisted they were not coming back from abroad where they live should we continue the pregnancy however they are pushing the court case heavily. Where do I stand? I have worked with social services after my mum and friend reported him as well as my psychologist from the perinatal mental health team who has worked out I was being abused since I have tried to cover it up for the last 6 months. Social services closed the case as I had left to my mums. If any more info is needed please ask as I need the best advice possible from this community. I suffer from PTSD, Panic disorder and a heart condition and this stress is killing me- which he knows. TIA