You do not have space for an island do a peninsula or even a galley kitchen. Get an actual kitchen designer they will help make the best use of your space . Not a cabinet sales shop but a real KD.

is that a window next to a door? you need both? is there a pantry going on that wall next to window?

do you have anything in the current space? any photos?

Get a counter-depth fridge and you won't be blocking the window--the fridge will just overlap it. As for the island, with the fridge on the other wall, you can move it a couple inches toward the sink; NKBA recommended minimum for a work aisle is 42" or 3'6", and you now have it marked 3'8". You need every inch you can get, behind the island seating.

How is the island configured? If you think 36" will be a 24" deep cabinet and 12" overhang, it's not measured just by the cabinet box. You'll need at least a 1" counter overhang on the front, and a back panel--so seating overhang will be only 10-11". NKBA recommended minimum seating overhang, for comfort, is 15". (Link to follow.)