The kitchen needs a peninsula, not an island where you play ring around the rosy to access the fridge and pantry. Center the range hood on the back wall, after subtracting the depth of the wall cabinets on the right wall. Tile the whole wall. It doesn’t need anything else.

What program did you use to create your layout?

I understand what you mean about a peninsula but it won’t work because there is a sun a room off the kitchen. Weird space I know. Working with what I have.

That is the IKEA kitchen planner

The island does not work at sll. So that leaves you with a simple 2 wall galley kitchen. But there is absolutely no reason that a peninsula won’t work. You are just not designing it correctly to work. You don’t know what you don’t know. You need an experienced kitchen designer to do the design work for you.

clear everything offf the window/sunroom wall on the right. butt the cabinets to right of cooktop into that corner. place sink in island . island could perhaps work if you have 12 feet across the room from fridge wall to window wall. show your measurements. adjusting things on fridge wall can also allow some 12 in deep cabinetry in the right spot to make walking aisle around an island an adequate distance. to get the best advice here show your mock up in terms of measurements of cabs/appliances//openings of doorways and windows and distances across and so on.

Here is the top down layout.

Sketch

White box will be a 40 inch hood (natural or painted)
Corner Shelving

41 inches all around the island