To put an ad ANYWHERE is taking it up a few steps from "looking" imo, and apparently family isn't as important to him, as it is to the poor op of this thread. I feel very sorry for you, and what I know you're going through right now.
I may be slightly colored in my opinions, since I've been at the wrong end of something like this 15+ years ago (though the final step was taken in my case, and it ended in a very nasty divorce. Had the final step not been taken, it would still have ended in a divorce, but probably less nasty.) Once you've been there, you know what it means, and what it really does to a person, whether you're a man or a woman. I'm one of the people, whose parents were married for 45+ years, til death did them part, and because of that, have probably been very naive, thinking that it's actually possible, to be in a relationship for life.
You put all your trust in another human being, which is not an easy thing to do in the first place. It takes a long time to build that 100% trust, and let me tell you, if you get there, and that trust is broken, it will stay broken forever, unless you're made of something that doesn't exist, and living in a relationship, where the trust is broken ... again, in my humble opinion...is 100 times worse, than not living in a relationship at all. When the trust is broken, the relationship is broken.
Not only does it break the relationship you're in, but you carry it with you. You take it to your next relationship. Try building that unconditional trust in another human being, after being treated like a piece of garbage, the last time you did it.
I know people are different, but from my perspective, saying that you're over reacting is like giving you another smack in the face. There IS no over reacting. He should be on his knees, begging you to forgive his stupidity and poor judgement. He has no idea what he has done to you, and judging from his reaction, he doesn't care. He is extremely selfish, and has no interest in a true relationship with you. If he did, he would have worked on your relationship, rather than looking for ways out of it (sorry if this sounds harsh, but you asked for opinions).
You basically have a lot of questions to ask yourself.. Can you ever trust this person again ? Can you live in a relationship, and can your kids, where this will be in the back of your head again and again ? Do you really still love this person, knowing that this is what he may be doing....you know for a fact that he HAS been doing it. Can you put that aside, and honestly say that you love this person, or is this now based on feeling safe in a relationship of any kind, rather than being on your own, with your kids ?
You are the only one who can answer those questions (and more), and trust me, i don't envy you even having to ask yourself those questions.
I hope you have someone you can talk to, and hope you and your kids get through this in the best possible way.
To the people who think this person is over reacting....we can talk, once you've been there.
I got to agree on this one tbh.
Looking and doing are two completely different things as KK says.
Maybe it's the time now to say 'hey, he's mine, wth am i going to do to keep him interested?'
Don't give up....family is way too important