hi seriously,
I understand your anger. Whilst my ptsd partner has never cheated, a few others have, and you are gith, they deserve everything they get from that. I am upset that he did this not only to you but to your children as well. I personally think that your idea about supervised visits is a wise one to make. If I were in the same opinion, I am positive I would do the same thing.
regarding your comment about his trying to blame you- all you have to remember is that you have done nothing but support him and try to keep your family together; he is the one who needs to assess his life and I think some serious apologising is on order on his part, whether you are willing to accept that or not.

My thoughts are with you and your children
Tammy