My parents married very young (18 and 20) and there was infidelity on both sides, but much more so on my dad's. Their marriage ultimately ended in divorce when my mum kicked him out. My sister and I were young adults by then but were relieved. After the initial turmoil of the divorce, mum and dad were able to be friends fine; mum remarried several years later and dad used to visit my mum and stepdad occasionally and they would also stay with him.
Your problem is that once the affair line has been crossed, it is so, so easy for it to be crossed again. You know you cannot trust your H. He has proved it twice. So, overall no - I don't think your marriage can be salvaged. He didn't care enough about you to stop the affair first time - he now says it's over but only because he got into trouble with his boss.
Look - you don't have to make a decision now. You're obviously not ready to do so. So just don't. And tell him you're not ready to make a decision yet and he will just have to live with the uncertainty - he has caused this, not you.
But I suggest that you ask him to move into a different bedroom if you can (tell the children he's snoring or something) and start concentrating on what you like and what interests you. Don't think of it as you pushing him into her arms - he's already shown that if he wants to go to her, he will do so, irrespective of anything you're doing or not doing.
If your children are 15 and 16, they will be pretty independent. Focus on yourself for a bit. Take your H out of the equation. You need to rediscover yourself. The more you rediscover yourself, the more you will trust that you can deal with whatever is ahead - whether it's continuing in the marriage or divorce.
What interests you? Cinema/theatre/night classes/choir/travel/seeing friends? Anything. Identify things which interest you/which you enjoy doing and go and do them. Without your H.
At the moment, he's convinced he can treat you however the hell he likes and you will suck it up. He doesn't think of you as a separate person. Show him and yourself (mainly yourself) that you are an independent, adult woman with her own life and interests and you will live that life the way that works best for her. Screw him. It's your time now. And yes, you should confide in someone. You need that outlet. It will help you think more clearly and make better decisions.
And if, in due course, you decide you need to divorce, your children will get over it. My sister and I felt loyalty to mum but we have a great relationship with our dad and mum was always very happy for that to be the case. Your children are old enough to understand that what happens in your marriage to their father is a separate thing to your and his relationships with them. Don't make them the reason you stay - it's an excuse and it's not fair on them.