I understand where pps are coming from but you need to be prepared for a harsh truth.
Unfortunately legally and in reality you can't make him love his kids or see them, parent them. I learnt this the hard way when I dumped my ex for cheating. He made a pretence of seeming like a "good dad" initially but it didn't last long and I tried various things to get him to stay in contact and have a relationship with dd but he now hasn't seen her for several years.
Sounds like I'm being harsh but that's the reality.
Even if it goes to court re contact all that is legally binding is you making them available for contact, nobody can make him show up and be a decent dad.
IF he wants contact it's NOT in what is now by his actions YOUR home, he takes the kids out or to his.
AND on a regular basis. He DOES NOT get to just show up whenever the fuck he fancies at a moments notice! That's not fair or stable for you or DC.
Financially is a different matter. Find and collate as much financial info as possible, all bank accounts, savings, investments and pension info.
The legal default is 50/50 BUT as you're likely to be the main carer for the children and he has legal financial responsibility to them you may well end up with more - do NOT recoil from that idea or EVER feel like you're screwing him over you're not!
Block the mil she can fuck right off! His cheating is NOT your fault.
It's a horrible situation to be in. Sleep and eat and drink as much as you can, make life easy for yourself, have ready meals or soups etc get support from GP if you need to.
And keep posting here sadly as you can see there's far too many of us.
Hopefully we can help you avoid any mistakes we made.