Why is there a laundry basket in the mud room space? Do people bring their stuff down from their bedrooms to here??

That was meant to be a laundry/folding table with a shelf (or shelves) to put a laundry basket which is 27".

A front load washer/dryer takes about 60" with door open and you obviously need space to stand in front of them. So if you could put them against the back wall of the 7'5" wall, you could put a folding rack on top of them and a hanging area next to them. I think your original idea would work fine as well.

Your drawing is not to scale and as Jan indicated, she is not sure of how wide the space is you have allocated for the washer and dryer in your first sketch.

So how wide and how deep is the space where you have your W?D and side door located?