The reason your H doesn't want to be put under a microscope is that he wants to be able to continue his secret, private life that is ultimatly incompatible with a healthy M.
I agree with Ellie on all counts.
I would also add that the chances you know "everything" are close to nil. It is far, far, far more likely that this is just the tip of the iceberg.
This sitch is not good for anyone. Get out of it. Protect you and your kids legally. Consider reconcilliation only under the conditions Ellie suggests. Seeing a shrink once doesn't count as treatment, either. He needs to be successfully working some program for sex and gambling addicts for several months before you should even think about the possibility of trying out reconcilliation.
As for STDs, condoms during intercourse do not protect against all STDs. They provide little protection against herpes, for instance. Moreover, AIDS can be transmitted orally, and condoms are seldom used in such cases.
You have NO IDEA what H has been doing or where his body parts have been. YOU CANNOT TRUST HIM ON THESE MATTERS. HE IS STILL LYING TO YOU.