H is out of the house

[MrBond]

"H sent a text saying "I am sorry for being a bad husband and hurting you, how are the twins and Lilly?"

I don't think this deserves a response."

It doesn't.

"When do you think I should contact H and set up a time for him to see the kids? Wait for him to ask or tell him "on Tuesday from 6 til 9 you are welcome to come see the kids"

Don't go out of your way to accommodate him or make him see the kids. Leave that up to him. He has to earn the trust back with you.