Scout, think for a minute about what you would do if someone told you about some other man who would not give his ex-wife his address at all, let alone when her child was staying there. That is weird and scary and potentially dangerous. It is insane. Your thinking so much about it or excusing it in any way is LBS egg-shelling. I know because I did it for seven years.
They unravel more and more as the D unfolds. Do not wait, do not pass go! Protect your child here and now with a solid arrangement and, if possible, a social worker who can either supervise H or ensure that he follows normal rules. The years to come will be a very vulnerable time for you kid, and your H may get worse and worse before he comes out of this. You don't have to be mean to H or sink to some low level that you abhore, but I would get things on paper, including where he lives.
I believe I will see the bounty of the Lord in the land of the living. Wait for the Lord with courage. Be stouthearted, and wait for the Lord.