I think you need to take a few long, deep breaths.
So, you and your children live in your own place, you haven't had to move? Good.
You were with this man eighteen months and moved him in? Too soon.
He's gone from the house now? Good.
His ex is a red herring. It's his behaviour that matters, because it affects you and shows how he is thinking. Forget her, she's irrelevant. Expecting to be 'friends' with his ex and expecting her to have a good opinion of you is unreasonable, even if you met him after he split with her. Feelings are involved. She isn't going to love you.
Don't write to the ex. He is an autonomous being and your relationship is with him, not her. You and she can't decide between you that he will be with you, which is what you seem to want.
You aren't of the same religious belief? That's a problem if one of you cares. If neither of you are religious, or both are tolerant, it doesn't matter. But it's a red flag if it means your expectations are different.
You want/expect him to have his own flat but to live with you and your children except when his children are with him. That's a bit controlling. It also puts you in the position of potentially being massively abused, taken advantage of. You'd be providing home comforts and sex for what? OK, if it's freely for your own pleasure... but why inflict this man on your children?
His being absent isn't 'all because his ex' this or that. It's his choice.
More deep breaths.
Sort out what kind of life you want before you speak to him tonight.
I'd suggest you tell him to stay in his own flat, not ever come to yours - certainly don't drop round for sex, food, washing, whatever - and that if he wants to date you, nicely, he can. At his expense. To give you pleasure.
Put yourself first.