I think you are right, you do need a prep sink. Either location would work but I suspect you will have more prep space if you put the prep sink in the island - the space between the range and the other possible sink location looks a little tight.

If you put the prep sink in the island move it down some so you have a landing space for things coming out of the fridge.

The seats at each end of the island will not work. Think about leg space. People can not share the same leg space.

I have a prep sink on my range wall. There is a nice bit of space between sink and range. It's a good arrangement for me. You don't really have room though so I'd center the range and put the prep centered on the island if you are sticking with that general layout.

Your overall layout, no matter where you put your prep sink, seems difficult to work in and awkward. How attached to it are you? :)

I would put the prep sink in the island, and agree with vinmarks that it needs to move it out of the corner a bit. Are you sure you have clearance for seating across from the cleanup sink and fridge? Seems tight to me.