Christ what a week op, you've been to hell and back and this shows no signs of stopping, he's completely kicked you in the stomach and is continuing to do so with his words and actions.
Your poor children, he's a dreadful father and a completely unsafe husband and partner, what a wanker, you must hate him and probably love him at the same time.
I can't quite believe he's asked to date you, he's obviously got used to the high octane lifestyle of cheating, lying and being a complete bastard and thinks you should be up there with him, continuing to support his fantasy meltdown.
Now breathe....
You do not have to do fuck all for this man, it won't make a jot of difference at the moment anyway because he's away with the fairies, he's going to come back down to earth one day but not yet, and I know you want the pain to stop, anything to regain some equalibrium and get your strength back, do whatever you need to do but your actions can be as meaningless as his were to your marriage, use him to pull yourself up if needs be, this is survival time, make sure you eat, drink and sleep.
Maybe you want to get him back just to screw their relationship up, do it, nobody will judge you and hopefully discard him later.
Just remember though you are going to change, your feeling towards him will change and from that you may change direction, I hope you gather some strength together, but in your own time, you need to recover from this devastating blow.
What he's done and how he's done it is so cruel, don't forget that, I'm sure you won't.
Keep posting for support, I wish you and your children well. Be aware of how traumatic this has been on all of you, the stress in your home must be off the scale, that man does not deserve to waltz back into cozy rooms.