Doesn't reply to me when he's with his babymomma

My boyfriend is naturally a dick and out of nowhere he started being nice to me. He called out of work on Saturday, ghosted me the whole day. Started picking me up to and from work. Out of nowhere without being asked. Things he never did. Part of me believes he cheated on me on Saturday and that's why he started acting all nice out of nowhere. Keep in mind we fought Saturday and I accused him of cheating.

I'm always tired. When I'm not at work I'm at school, if not at home w my daughter. Today he worked double shift and I worked closing shift. He sent me a msg at 4pm saying he was at work. Didn't msg me since. I got off at 9 and at 9:15 he called me to tell me his daughter was at the hospital. I couldnt hear what he was telling me because I was in the train, all I heard was his daughter was sick and somewhere. I responded "i can't hear you.. your daughter is in the hospital?!" And he responded " NOOO. She's at the bakery with you. You're so fucking stupid." I ignored his comment and said "hope she gets better. Goodnight"

Now he ruined my night because I know he's going to be with his babymomma all night I assume at the hospital. And now that explains why he doesn't reply to my msgs. Everytime he's with her he doesn't reply which I find very strange. The day he called out/disappeared he didn't reply the whole day. Said he was going to run some errands and just last night he told he slept the whole day. Lied, got caught up on his own lies. Yesterday was his day off. Didn't reply the whole day. Said he was in his bed the whole day but he came to pick up he said he was so tired and sleepy. How if you were supposedly asleep?

Seems like he's cheating right? How do I catch him? I can't prove anything it's just a gut instinct.