The door from the kitchen to the utility room (or also pantry, right) could also be implemented as a hidden door as part of the kitchen planning, then it looks like a kitchen cabinet door, only it leads to the utility room. Carrying laundry around could be solved with a laundry chute from the bathroom.
I would design the fireplace in the living and dining room a bit as a room divider, making the living room cozier without taking away the open space.
Moving the stairs because of dirty shoes? Mmmmh, there are households where people take off their dirty shoes. If the kids don’t want to take off their shoes, a pointed hint to the kids: there is still the baby hatch, you can keep your shoes on.