Is my baby father / boyfriend cheating?

Hello all. I delivered twins 3 weeks ago and I decided to come and live with my baby father and told him I wanted to work on our relationship for our kids and he agreed and we started dating again. But ever since I came back , this girl named monique has been texting him. And when I seen her name pop up, I said who’s that? And he said that’s my aunt ... and so then I noticed he was texting her for 3 days straight so then I told him “you don’t text your aunt for 3 days straight “ then 3 days later he finally tells me the truth and says that’s a girl he was messing with before I decided to come back. He’s still texting her and he has her car and pays her for it , don’t you think that’s really risky? And second he doesn’t even sleep at his house with me , he claims he’s sleeping in his car all night because one he’s not with me and 2 he doesn’t even answer his phone if he’s sleeping in his so called car which is her car. So basically he’s still dealing with her and trying to deal with me at the same time but claims he doesn’t want her. I’ve asked him to block her and everything and told him to give her her car back. And he says “No” so clearly he wants her. I don’t think she even knows about me or about our new born premature twins. I am at the hospital everyday for my babies. I’m the one getting things ready for their arrival home. (They are currently in the NICU still) they were born July 17th and from that date hes never went to the hospital to visit them. He started coming in early August but stopped and said “I don’t like seeing my kids like this” no it’s That he must be with that girl all day long and uses that as an excuse. He lies about everything and thinks I’m so stupid like who so called “sleeps in their car all night long when they have their own place” like that makes no sense. I definitely know he’s cheating. What do you guys think? How does this sound to you? Btw he hasn’t been home to sleep with me in 4 days now and hasn’t come home tonight.