'That said, will I ever feel better even if he moves? will it just be someone else that takes his fancy?'
After only four years together, with three children to think about too? And she's half his age? And he's 'flirty', and describing this as 'just got out of hand'? And he didn't confess, and you think that if you hadn't rumbled him it would still be going on?
Yes, it probably will be a case of waiting for the next one to come along, I'm afraid.
Basically, his attitude says he slipped up. He doesnt think flirting (essentially, disrespecting you and your family on a daily basis) is a problem. You just have to draw the line before it technically becomes cheating. Ooh, naughty boy!!
He's not a keeper, OP.
It's up to you what you do. You could let her family know - I think I probably would, not a popular opinion on here generally, but I would feel just as sorry for her poor new husband as I do to you and would think it were the right thing to do to let him know what he's shackled himself to before he has a family with her.
You could ask your H to move out - whether he would might tell you a lot - an angry refusal is basically him saying tough, I'll act sorry but hey, you have no real right to disrupt my life - I'm more important than you and I don't really have a problem with what I did. That will tell you EVERYTHING.
You could try and push this down and suck it up, as you are doing - I don't think it will work long term.
Sorry this is so negative. It's just that every single aspect of this says that this guy is a wrong 'un - a disrespectful, selfish flirt and a cheat.
Good luck with whatever you decide to do. You will always find good advice and support here, though.