CW - I know how hard it is to keep your hope up when there is so little positive to go on. Just remember...the affair has to play-out and him moving in with the OW may speed it up.
My H was really upset when I brought up that we will have to sell the house. He didn't want to do it. Yours doesn't like it either...he won't say much now...let it fester.
I wouldn't bail him out about talking to the kids. Let him explain to them what he is doing. When my H decided to leave us I told him that we should both be there together when HE tells D. If you are present you will hear what he is telling them and he can't spin things to much.
The positive I see in your sitch is that you are able to talk calmly together and he is helping with the house and wants to be involved with the kids.
So take a deep breath and continue on your path.
M53 H54 D17 M33Y T38Y Bomb OW 09/09 OUT 10/09 BACK 11/09 OUT 01/10 WANTS TO R 04/10 BACK with OW 05/10 Wants to Reconcile 05/11 I said NO