It seems to me like your father is dealing with some kind of mental illness. They come in many varieties and severities. Some, like bi-polar disorder are intermitten and the person will have periods of "normality" and periods of paranoia, anxiety, depression, manic episodes, etc. Having lived in Queens I understand the desire to not lose a parking space - to a degree - clearly not the degree you dad had. But if your dad has a mental illness the anxiety of losing the parking space can be overwhelming. It's not normal clearly - but it can be a reality to him.
I am not suggesting that your emotions about your dad are invalid. Clearly his responses to you over the year have not been normal and have been hurtful. But if you understand that they are coming from a man with a diseased brain it will help you to NOT take it personally. He was not making a rational decision against you. He was making bad decisions based on a sick mind.
You are entitled to response however you want. You need to be healthy emotionally in order to be a good mom. You are not obligated to go out of your way to develop a relationship with him. I would suggest, however, that instead of holding on to a bitterness towards him that you forgive him (that is NOT to say that he wasn't wrong - he was) and allow yourself to heal. We tend to have this wrong thinking about forgiveness - that by forgiving someone that somehow we "let them off the hook" or that we can't forget what they've done to hurt us, etc. In reality we become more healthy by extending grace (undeserved merit) towards a person that hurt us - and moving on. Our minds will never allow us to truly forget - but we can put it behind us.
I don't think it's a bad idea if you happen to see him at a family gathering - there would be a buffer of other people around to cushion any anxiety or awkwardness. But, no, you do not need to have him in your life if you don't want to.
My story with my dad is that he left our family and moved across the coutnry with his much younger new wife, adopted her children and had another with her. He never paid child support. My mom was vision impaired (since childhood) and was in the midst of needing spinal surgery at the time he left. We were on welfare & food stamps for a few years while my mom got job training and ended up as a nurses aid working midnights for the next 20+ years. We saw my dad once during that 20 year period. Almost 20 years later he came back to the east coast to visit and I refused to let him off without an explanation. So the night he arrived I picked him up at JFK airport and sat him down on my couch and asked him "what were you thinking? How could you leave 5 kids and your wife? Didn't you miss us or feel bad or anything? He broke down in tears and expressed great remorse. He had suffered a mental breakdown and spent time in a psych facility. He had tremendous regrets over what he had done and how he left his kids. I did forgive him. He told me how much he loved me and how much he loved his kids and how foolish he had been. We managed a small relationship - but I had explained that our mom had earned our respect and time and he could have a relationship with me but it would never be all that close due to all the lost time and pain. I went through many failed relationships and chose damaged guys as mates as a result of his decisions. But - God is good and He has restored the years the locust destroyed.
My dad died only a few years after that conversation I had with him. I was glad that I had had that discussion and knew that he loved me and had suffered anguish and pain as a result of his poor decisions. I was able to deal with his death without regrets about my actions - only about the lost time and what could have been - but none of the regrets were about anything I could have done differently.
My FIL was physically abusive to my husband - and it took a long time for my husband to get past that pain. But my FIL was a much better grandfather than father and my children were blessed to have a grandfather in their life who adored them. They never saw his flaws, only his positive characteristics - which was a blessing for them (&him). My husband was also able to bury his father without regrets.
Personally I think you'll be healthier emotionally if you can find it in your heart to see him as a really flawed person - probably with a mental illness, forgive him and move on. He may make a wonderful grandfather and that would be a good thing for you child to have another person in her life who loves her. But you are under no obligation to have him in your life. None. Only you know what you have the capacity to handle. If not now, maybe in the future.
Good luck mama - this is some of the tough stuff of life. My prayers are with you for wisdom and discernment.