Stop beating yourself up dear.
I am glad to hear that you are seeing a therapist. Continue seeing a therapist.
If you continue having sex it’s your business, not for anyone to judge, but I urge you to use protection. If he is unfaithful, it’s too dangerous. Sadly I knew a lady who worked with HIV/AIDS foundation and was an advocate for HIV patients, she contracted HIV from her own unfaithful husband. She wasn’t sick for a long time but then AIDS kicked in. She didn’t know he had it from his affairs as she had no clue he cheated. But if you do know, try to be careful. You got to be well for your children! Most people contract STDs not from one night stand with strangers but from their own unfaithful partners. I am not trying to scare you. It’s perfectly fine to have sex with him, why not? but protection will keep you at least somewhat safer
You do what you got to do
It’s sad though that he isn’t interacting with his kids.

I hope he could make some changes in that department and spend more time with kids