Op you're not some young girl out in the workplace, naive and inexperienced enough to be taken in by lines that neanderthal man was using to get his bit on the side (and they already old lines when he was using them) ... You are a mum of two kids, you have life experience, you have responsibilities ... Don't be letting men like this fuck you around and upset you.
You say you're jealous, that the situation is really badly affecting your life, you're clearly unhappy .. and no wonder in a situation like this. Thus is affecting your mental health and happiness and by default it's probably affecting your parenting. Hard to be a fully present, relaxed, confident, happy parent when you're unhappy. It's not fair on you and it's not fair on your kids.
Get rid of him. If he hasn't left by now he's unlikely to, if it's all soul mates and blah blah, he will finish his relationship sooner or later and come after you. If he does that and truly stays finished you could consider entertaining him. I don't think he will.
Even if he did, he's still a cheater and I doubt you were his only illicit ons.
Get rid of him, take some power back. He's got it all) you've given him it all.
The only way to fall out of "love" is to stop seeing the person, stop being intimate with them, try meeting other people (don't rush into anything, just be aware there are other possible partners out there for you).
And forget about "winning" against at his wife, there was never a real competition for the simple matter that he met and got into a relationship with and had kids with her first .. so he's invested and leaving her has lots of disadvantages he's likely not prepared to take. And just think; if he'd met, gotten involved with and had kids with you first; you'd probably be the one being cheated on. No-one's all that special, esp to men like him.