Is it done?

Okay so about six months ago my boyfriend was out here trying to cheat, I found out before he actually cheated (I think) it was just a lot of messages, naked photos ect. We have just had a baby so put her first and agreed to work on things. They are both still liking each others posts on socials! Am I insane to want to break up because of that? It feels really disrespectful. Like if he's not even willing to unfriend her on insta then he's not trying, that's like bare minimum right? I need someone to be blunt with me because I feel bad for our daughter being split between the two of us, she's only just turned one 😞