How do I expose the affair

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Here is a convo I had with H last night. I had to call him to set-up who was getting kids after school today.

H: What is your plans with the kids?
Me: See them tomorrow night and then again on Thursday
H: And then what, every other weekend?
Me: No, I would like to have them back full-time. I'm doing much better and I'm ready.
H: How is that going to work, are you getting your own place?
Me: Well that is something I wanted to talk to you about. I've thought about it, and I finally agree with what you were saying about me trying to keep the house. I've gone over my budget, and I think I can do it.
H: I thought you said the house was to much and it stressed you out.
Me: It wasn't the house, it was what was happening to our M that was stressing me out
H: Is that how you want me to change it in the D papers (he had them already written up with him taking the house)
Me: You change it however you want. I've told you how I feel about getting a D. I was thinking of moving back the weekend of April 9th.
H: No, that won't work
Me: Oh, do you want me to move back in this week
H: No, I need to find my own place first. What about getting our D a 4-wheeler for her bday?
Me: That is not a sound finicial decision that I can make right now. If you want to get her one, you'll need to figure that out.
H: K, fine.

He sounded very angry about the whole thing. I really didn't want to tell him that yet, but I felt it was the right time because of what he was asking me. I do feel better now that I have told him it though.