May, i'm so sorry youre in this mess and in this pain.
if you're sure, and if your boundary has been crossed, then you have 2 choices: stay and forgive - which doesnt sound like an option and thats fine, OR leave - if he crossed the line, then yes, you're absolutely within your right to make the decision to walk away.
neither choice is wrong, you just need to figure out which one is right for you.
and yes its going to hurt like a b@tch for a long time. but it does get better.
my x cheated, i had proof from the beginning, but i made the mistake of trying to save the marriage. and even if i saved it, i would have ended it eventually because i can never forgive her for what she did.
to me cheating is unforgivable, initially i had thought i could forgive her and get past it, the fear of being alone made me believe it, but when that fear passed it would have always eaten away at my mind. to others, they can work past it. i cannot.
and i too thought about ending it all, those thoughts have always been a part of me, but ultimately the x wasnt worth it. and my daughter most absolutely needs me. as yours does.
"In a ham and eggs breakfast, the hen is involved, but the pig is committed".