If he is only “window shopping” then is that still classified as cheating? He’s not actually doing the deed…
Or is he? 
I’ve lost count of the amount of times i’ve said this - “each to his own”.
Having said that, if i was in that position, i would hope that he would have the decency to tell me first. If not, to hell with him! As long as he is there for my children, is a prominent father figure and supports them, then fine by me.
I’d hate him, yes. I’d be broken, yes. Would i seek revenge of some sort? In the heat of the moment, most probably. But i would hope that i would pick myself up and carry on with life. My children are my life. I live and breathe for them. Husbands can come and go as they please for all i care. 
(If you’re reading Mr Maroush, i heart thee 
)