Am I justified in wrecking my home?

I have to 2 kids with my bf of 4 years and we’ve had problems with him talking to other females and exes in the past. More times than I can count. A couple days ago he’s following his ex so I ask to see his ig dms to see if they’ve been talking and I noticed from last time a woman he’d been talking to. Last time it was just 😍 each other’s stories and hearting it. I noticed they’d been talking he deleted all the heart eyes from last time. This time is was pretty innocent just hearting every message. I told him I’m uncomfortable with it and asked he block her. He did then ended up adding her back and blocking me instead. Between the recurring ex and now this new lady is contemplating leaving but I don’t know if I’m justified in breaking up my home. He’s never physically cheated.

My mil says all men need to flirt and it’s innocent. He deleted messages out of respect. Basically as long as he comes home to me then I should be happy. I’m just not. I cant handle him flirting with other women, it hurts me. I’m not strong enough