Bf leaving me and 5 week old?

I’ve been w him for 2.5 years . He hasn’t been the trustworthy (girls popping up on his phone, videos of him grinding w a girl in a bikini on social media from put n bay, lies) during the first year.

Then we broke up a year ago for a week when we got back together he changed and committed to me. Then I got pregnant and he has been great . He has a 7 year old who lives w us on the weekends. (They live in my house)

Well we have a 5 week old who is colicky. It’s been hard, but we’ve been ok. At times he gets mad at me bc he says i critique his skillls (he tells baby to shut up) he thinks since he’s been through this before he’s got to, which he’s great ..

The other day I found out he was messaging w his x fuck buddy (she’s popped up before ) on linked in. He searched her. The convo was brief but that’s because he was doing it while driving home.. he got home so it stopped prob.. I didn’t say anything right away I wanted to see if it continued . It didn’t .. well he found out I knew.. he came home and asked for our son and I said we were good laying here. He went outside for awhile then came in and was packing his stuff. I got our baby to sleep and then went to him and said we need to talk.. he wouldn’t talk. Then I said why were you talking to her. He said she messaged him so he said what and she told him he must miss her he said he said whatever’s I said ok..I have proof he searched her first, but whatever .. I tried dropping it. He’s like you wouldn’t let me see my son when I got home, so I went and got him and they passed out on the couch together.... his car is still packed when he left for work today... idk what to think .. idk if he’s coming home today or what..