Not only is he cheating on you, he doesn't even respect you enough to hide it well. If you can be part of it offer it to him. If you can live with it, set rules/boundaries and have open relationship. If you can't neither kick his sorry cheating ass out the window.

Well OP, I don't know how to say this without sounding mean, but you are stupid.

keep forgiving him of course he’s making it a habit out of it. I feel sorry for you. Make up your mind already and think things through.

Please find a way to leave him. Don't stick around for the 5th time. FYL but if you stay knowing this is what you're getting YDI

YDI. The saying “Fool me once, shame on you, fool me twice, shame on me” comes into play. I’ll add “fool me thrice, I’m an idiot”, and “fool me fourth, YDI”

OK for those saying YDI, please bear in mind there are 3! children involved and it's a good possibility OP cannot make ends meet on their own, especially with 3 children. She may very well be trapped in this untenable situation for the time being. Don't be so hasty to judge.

why didn't you leave the first time? it doesn't matter how long you've been together or if you have kids with him. leave. You'll be doing your children a favor

I'm sorry, but if he did it once, he'll do it again. And he's proven that. Unless you're okay with an open marriage, it's time to kick him to the curb.

and he's going to keep doing it because you keep tolerating it

I feel so sorry for you OP! I can't imagine how hard it must be after so many years together and even with 3 children! him choosing to marry you and getting kids with you to just use your kindness now! I myself have no idea what I would do... you not dumping him right away, I totally understand since you're tied together so strongly and it must be devastating having to deal with it... I wish you the best OP, no matter what happens!