caught my boyfriend cheating..

hey there guys and gals, (happened 5 weeks ago) Long back story short: boyfriend was married, walked in on his wife cheating, met me, got a divorce now we live together. Liam and I were doing great! so I thought.. he was out helping a good friend of his and left one of his phones at the house, has one for work and his personal. I had this aching feeling to check his phone and I didn't expect to find anything.. I did.. now I must emphasis that it was only messaging (at least to my knowledge)... there were pictures exchanged and he sent a video... a motherf****** video. I felt like I got hit with a sledgehammer on my chest... couldn't breathe for a good 30 seconds... I was so confused.. I didn't cry... is that bad? I wasn't angry.. I was just confused.. when he got home, we talked about it.. I decided to stay... but I wanted to leave... (present) todaaaaayyyyyyy, he tells me that they talked about the video that was sent as well as the pictures. she tells him that I should know and he tells her I already do know and I decided to stay, she called me young.. 😡😡😡😡😡😡 ANYWAYS!!!!!!!! She tells him to tell me that shes sorry and that it won't happen again... I seriously almost wanna ask her for a face to face apology because if she really meant it, she would apologize face to face right? I've never met this woman, not yet.. now my issue is and I need opinions... honest opinions...ever since then he has been more affectionate and just showing me that he seems to be in this relationship... do you think he's doing this just to get on my good side so that way I don't expect him to do it again and i wont suspect him if he is ?? Or is he doing it because he's really truly sorry..??? help... (I failed to mention one thing. they have two kids)