Here's my take on cooking: If you cook a nice dinner for yourself and kids and he's there, I would think it's a good thing if he chooses to eat with you. He sounds like he is torn on how to proceed and what he wants, and you're letting him figure it out for himself, BUT showing him what you and family life has to offer. Him eating with you and your kids is a normal family activity that is bound to keep at the front of his mind what he will be missing out on. He goes to OW with a reminder of you still fresh in his mind and belly.
The way to a man's heart goes through the stomach, they say - that's very true for my H, he puts a lot (much more than I could ever imagine) of meaning into whether I cook dinner for him or not.
M 16 yrs, WH62, P54 3 adult blended kids EA 11/13, BD1 6/14 PA fall 14, BD2 2/15 Piecing 2015, BD3 12/15 Separated 4/16 WH moved OW in 5/16 Divorced 6/15/17