No judgement here Darling, take a deep and give your own self time to heal from this and learn about yourself x
New relationships are easy. The excitement, touch, butterflies. That's why they call it 'Falling in Love', because you are 'Falling', it's easy, no work is needed, it's fun.
But being in a relationship, in a Marriage, is damn hard work. And sometimes, maybe all the time it seems like work. But learning to love each other for who they are and accepting things aren't always going to by rosy and easy for you both. It's teamwork and friendship that will get you through.
I'm not saying go back with your husband for your kids, hey, I'd rather come from a broken marriage than live in one, but give yourself the gift of trying absolutely everything in your power to work things out with him, in a friendly nonjudgmental way, so at least if things don't work out for you both, you gave it your best shot, and then can move forward with life xxx

As I said, no strong opinions on my behalf, but give the married man the arse, he doesn't deserve your energy and time. If being with your husband is that bad, focus on your kids, and healing yourself, not this guy.

Take care honey, I hope in the future you and your children can be happy xxx