Have him help with the kids bedtime while you spend 10 minutes doing your extra clean in the kitchen. I honestly don't think this should be a big issue if you're working together as a team.

There is a happy compromise between "move everything on the counters to clean" and "just kind of wipe up the spill". When DH or I clean up after cooking, we only do the area we used for cooking. Our counters are huge and would take far too long to move every object to clean. So if we used a small space, that small space gets cleaned up.
.as for the floor, if you are swiffering twice it's time to invest in something more hardy. It's also time to invest in those things you put over the pan to keep grease and oil from splattering everywhere.

Same situation here. I clean up after his cleaning. The person who wants it cleaner will always do this. I look at it like this: I have a light cleaning to do. He has done the heavy lifting.