Hopefully you can reassure the children that lots of things won’t change. They will still live in the same house with each other and you, go to the same schools, have the same friends.
Their dad will still be their dad and will still see them and live Elsewhere. Once their dad has sorted out where he’s living they might be able to go and stay with him some of the time, perhaps at weekends.
Once they get over the shock they will be ok and will adjust to the new normal . Lots of their school friends will also have separated parents and will tell them its ok. It’s a big change but most kids cope just fine.
I’m sure their father will be in touch With you later this week To talk about seeing them. Start the way you mean to go on and do NOT agree to him seeing them at your house. He can take them to wherever he is staying or out to MacDonald’s.
It’s not fair on the kids to let him into their home to play happy families. And you will end up making him Meals and coffee like a guest. Or worse, letting him make his own like he lives there. Mixed messages.
And you will end up hiding in your own bedroom to give them space or even going out. No no no.
He walked away from all these privileges when he put OW before his kids and his marriage.
I’d get him to come off the tenancy ASAP so he has no right to come in. Get back the key or change the locks once he’s off it. It’s great that you have a secure tenancy.
Be polite but business like. Don’t Cry beg or plead. Don’t ask him why he’s done it or where he’s staying or anything like that.
Save your tears and rants for MN or your best friend round with a bottle of wine. Or forums like chumplady.
If he comes to collect His things , do it when the children are out. DO NOT let them see it. Men like to act like the injured party - look at evil mummy evicting poor homeless daddy with all his worldly goods in black big bags !
I’d try to have a friend or relative there, either with you or instead of you. Less chance of drama that way. Preferably a large stoney face male.