This is a high-degree-of-difficulty request! :) No wall space, three car seats (do they never live in the car?), and more.

Is this whole space entry? e.g., is there any real furniture that would appear in the first photo, or is this all empty? what is the mat on the left in that shot?

Without closing up any windows, I'd say use the zone where the window is higher to set up a bunch of hooks and/or cubbies for coats and bags. Under the picture window you could put a long bench, with a mat/tray underneath for shoes and boots. (As the kids get older, this may need to evolve into more closed storage, but start small.) Add a chest on the wall by the door, where mittens and other small stuff can be stored.

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More suggestions with more info...

Just found this one -- if you can have furniture in the center of the space, something like this could make room for everybody to be changing shoes at once...

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