I’ve only read bits of this thread so I’m going to contribute my own experience and it may be totally irrelevant. But this is STW and I must be heard!
My parents stayed together for my sake until after I’d left uni. At times it was amusing how much they clearly hated each other but mostly it was just an unpleasant environment to grow up in. Looking back it’s clearly had a fairly large hand in making me the misanthrope I am today. Of course, they never asked me, but I think I could see the relationship was broken long before either of them could. I don’t remember them ever being happy as such, but it definitely got worse slowly over many years. I don’t know if it may have started out like the OP? Certainly I have subsequently heard bitter accusations of cheating, but to be frank I really don’t care about that. If one of my parents cheated, it wasn’t on me, it was on their spouse.
I guess what that boils down to is don’t stay together “for the kids”, stay together because it’s what both of you want. Or don’t. But leave the new woman out of the equation, you either want to stay married or you don’t.