Overall, this is a great idea and will much improve the function of the house. Thoughts:

* the new door from the garage into the living area must be fire rated per codes

* the new door from the garage into the living area would probably be more convenient moved as far left as possible

* the new door from the garage into the living area should be a perimeter security door with a deadbolt (I recommend Schlage keypad deadbolts)

* the new door from the garage into the living area could be made obscured glass to let more light into mudroom and vice versa (code requires this to be tempered safety glass)

* check for code compliance while you are doing this project (very strange layouts such as your current one raise the spectre of previous homeowner mods which may not have been code-compliant)

* lay out the exact laundry setup to make sure you allow enough room for sorting, folding, machine access, multiple baskets, storage etc.

* add a window for mud/laundry room

* add a utility sink

* include door sizes and door swing directions in your planning

* storage would best be open shelves to avoid becoming a dumping ground

* plan space for ALL mudroom activities and storage: pet feeding? winter coats and boots? toys and sports equipment?? etc.

* convenient lighting is a must - perhaps automatic lighting that turns on when room is in use and off otherwise (avoids need for multiple switches, turning lights on and off)

* given all the above, I recommend a hinged door from kitchen to mudroom (with obscured glass as above) to conceal the less-sightly activities going on in mudroom. Be sure to account for swing

Good luck!