Ex/new partner and baby almost here

I’m hoping to get some opinions on my situation if at all possible. I ended my relationship with my partner when I was only 3 months pregnant reasons being a lot but to name a few (verbal abuse like name calling, cheating,irresponsible with holding a job and picking fights with me every day over nonsense and zero respect for my child I have already who’s not his) to name a few things.

Well I unexpectedly fell for and got involved with someone who I have known for over a year and a half afterwords. He has been there for me in every way and has done nothing hit shown love for me and everything that comes with me. My ex has not offered to help with anything such as asking if I needed money for anything or to see how the baby is doing all he’s been doing is calling me repeatedly on blocked call multiple times a day. I know this because I have an app that registers his number even if it’s blocked, I seen his car drove past my house a few times as well and when I confronted him about both of these things he denied it (of coarse). I went ahead and told him regardless they I will get a restraining order if i still see it happening. It has since stopped. Anyways long story short I feel as if my partner in my life has earned and deserves to be a big part (as daddy) in this child’s life once born.

My ex is this child father and as much as it pains me to say I will have him around for her but I feel as if it won’t be the best as my ex is very immature doesn’t have his own place can’t hold a job and refuses to be an adult and acknowledge and keep peace between relationships as he can’t seem to keep on good terms with myself at that. It sucks as I feel I would need to go into more detail but you all would be reading all day lol. I just don’t know how to go about a situation such as this. If anyone has or knows someone that would be a huge help!