suff, he doesn't want you to file for divorce, of course he doesn't! He wants to know that you do really still love him and that the door is open for him to come back again should his feelings for the OW suddenly diminish. In other words, he wants to have his cake and eat it.
Stuff him - file for divorce when YOU want to, not some arbitrary point in the future when he decides it's ok after all! And if you haven't already done so, do go to a solicitor as well. Perhaps there is some kind of limitation on how long you can divorce on the grounds of adultery? Perhaps he is trying to get you past that point, so things go more in his favour? YOu need to check.
Well done for refusing to allow him to be alone in your home with the DC now - let him take the DC out for the day. Put some effort in, rather than coming back and playing "happy families" for the day as though nothing has changed.
As Peter says, stop trying to understand him - all you have to remember is that his motives are purely selfish. He doesn't want to lose you, but he can't give up the OW because his feelings are too strong? Well he can just fuck off over to her then, can't he! And if he realises he's made a mistake, well too bloody bad - because he should have realised what an arse he was being looooooong ago and stopped hurting his wife and family with his stupid selfishness.
Stay strong - I'm sorry that your H is such a selfish nobber and I hope that you can move on from him now that you know how little he values you and your relationship.
Oh, and if he comes out with any shite about her being "like a drug", or an addiction, or even his "soulmate" then you can just add that to his list of monumental stupidity.
Have an unMNly (((hug))).