Biological dad troubles...help!! Long story!!

A little back story. My mom & bio dad dated for a while they broke up before she knew she was pregnant. She reconnected with her HS sweetheart & they have now been married for 20 years. When my Bio dad found out about me he tried to be in my life a little but not consistently so my mom said he needed to be there enough so that I knew who he was or if he wasn’t ready to be a dad just to leave. He decided to leave when I was 2.

I always knew that my stepdad wasn’t my biological father but to me he was my dad. He had been there for as long as I could remember. My bio dad decided to get in touch with me 1 month after my 18 birthday.

I found out later it was because his new wife didn’t want to have to pay child support to my mom because of me (my mom never asked).

I finally met them & my half sister (mainly just to meet my sister) when I was 19. It wasn’t horrible we were all nervous but I could tell he just kinda wanted me around for show & I heard him tell someone that my mom had kept me from him & moved me away so I couldn’t see him & I finally found him a year ago! None of that was true I’ve lived in the same town my entire life & my mom always told me that if I ever wanted to find him i could growing up.

Fast forward 2 years later. I got married & im now pregnant with my first child. I’ve kept in touch over the years. I called & told them I was expecting just so they wouldn’t see it on Facebook. So recently he has made multiple comments about coming to stay with me so he can be in the room when the baby is born & be around for the first week or so. I’ve told him that I didn’t think that was a good idea because our house is small & I don’t want him around while I’m trying to get in a routine with my baby. No matter what I say he doesn’t seem to get it. I don’t know what to do. Any suggestions???