Please post the layout of the whole floor.

I like separate zones so would not move the sink and DW to the island. If possible I would move the refrigerator to the sink wall to eliminate zone crossing. If someone is prepping at the sink they won't have to cross behind the cook to retrieve items from the refrigerator. The DW can also be loaded/unloaded without interference. You might also want to consider a sink with ledges that can hold a cutting board.

It looks as if your idea will work, but I'd make a couple of tweaks to the island. Instead of 5 seats lined up on one side, make the island slightly smaller and put a seat at the end. Put the DW on the end near the perpendicular counter, for convenient dish storage and unloading. How wide is the aisle behind the seating?

If you reconsider a prep sink, you can have everything you want, plus separate zones:

@emilyam819

Here is the whole main floor, hope this helps.

If you are right handed, you might consider putting your dishwasher on the right side of the sink.

If you're not putting your washer and dryer in the mud room, you might consider leaving the mud room open to the kitchen and putting your refrigerator just inside the mudroom -- leaving the wall against the garage wall for cooking appliances.