He won't be telling her that you forced him to divorce.
He has been doing the double lying thing, telling both of you that he wants you and that the other one won't go - while he hedges his bets and is keeping her as a reserve.
So far he is letting her go ahead with planning wedding etc- what else could he do if he is staying with her parents? Tell her, oh I don't want to be with you, I've been begging my wife every day to take me back. Of course he's not 'trying' to end it with her because if he did he risks being homeless.
The main problem here is the childcare. It means he is around too much and in your house. You can't move on like this. He broke the marriage and has been dangling you both for the past year. Even if you did take him back he would probably keep her on on the side, spinning her some story about how he is martyring himself for the children and that if she will wait then they can be together when the children are older or some other shite like that.
You need to get an aupair or mothers help. Plenty of agencies to supply those.
Then tell him that as he caused the separation, and you are now divorcing him on the grounds of adultery, you expect things from now on to be as normal for a divorced couple. Tell him that he is no longer able to come to your house to look after the children as he does not live there any more. He will have to make arrangement as other single dads do, to have the children every other weekend and one night midweek. Tell him this will start next Wednesday and that he can pick them up from the end of the path and will not be entering the house.
I think I remember your thread from last year when you threw him out. I have seen some situations on mumsnet in the past 8 years but none as unbelievable as this, where a man is thrown out for having an affair then keeps the mistress on for months and months with full knowledge of the wife who claims not to be able to make up her mind whether to take him back or not!
He made that decision for you. When you threw him out he kept his other woman on. He didn't make enough effort to put things right, for you to even consider for one nanosecond that he could come back.
Move on, your marriage is gone. A lot of the last 14 years will have been good. But don't throw more time into the black hole that your husband has become.
You have a good job, that's more than a lot of cheated-on spouses have on these boards. Just get rid. CHange the locks, get an aupair, send the kids to stay with him for his visitation next weekend. I'm sure his new inlaws won't put up with that for long.