Did you post about this before? It seem familiar. I know I don't like to see the mess from the mud room on display, so I would not leave it open. I under stand the issue with bringing in groceries, but I think the door needs to go by the kitchen. You need to make it super easy for your kids to drop their stuff in the RIGHT space. Also, that is an odd placement for a laundry room. Any other options for that?

I like it how you have it with the pocket door to laundry and open to mudroom.

I'd probably do a large cased opening, though, keeping it as wide as possible (or at least put in a header to turn it into a doorway). It's a tad more formal and it makes the mudroom a separate room instead of "the back of the kitchen with shoes". (But it should go with the rest of the house--if you have open flowy connections between rooms everywhere then be consistent.)

IMO a door would make unloading groceries a pain and where the opening is I think it is fine to leave open as long as kids put stuff wher eit belongs. As for the kitchen IMO the walkway in front of the fridge is too narrow and I never like a sink and range directly across from each other without having a 60" walkway there if you must do it,

The advantages of a pocket door is that there is no swinging door in the way and that you slide it open as long as you need it and it stays out of the way until you want it closed. Since there is an outside entrance to the laundry, the laundry is essentially part of the mudroom. IMO, place the pocket door at the entrance to the kitchen.