what kind of a father and husband just leaves the family like that, not even asking if the kids are ok or anything?
don't worry about rent he will be made to oay child maintenance and it's unlikely he will want to take care of them considering he can leave them for days without a word. do you have a shared bank account? revenge is a dish best served cold, start saving, squirrel away anything you can, open a new account without him knowing, you and your kids deserve so much more, i'm so sorry, but i've been there before, not infidelity, but 10 years of toxic, narcissistic abuser, who traumatised me and the kids.
Leaving and starting again is scary, but the breath of fresh air, and weight lifted is insane, and one day you step back and can't believe how you put up with it, how amazing and different in such a good way life is, good luck and i hope you keep us posted.
I love a good escape story, finding your lost worth is life changing.
Do you have any parents you could stay with while you sort everything out?
i'd be stealing his phone and getting it unlocked at a mobile shop, proof to give to court etc