you would do an L using fridge wall and sink wall. You would eliminate the things on the side where the towel bar is attached to the end of the run. You would gain walking in/out of space on left and right of island which splits traffic and is a good thing. the orientation and dimensions of island can be adjusted as dimensions allow. run it up and down or perpendicular, in other words, to peninsula as shown, perhaps. You need to show dimensions of everything.

The space looks a little tight for an island. I had a peninsula in my last kitchen and loved it! I tried to do one on my current reno, but it interrupted the walking flow too much. So, we are doing an island. I am a little nervous that I am going to hate it because I like the wide open middle that a peninsula provides, but I am crossing my fingers and going with it.
Do you have a floor plan of the house with dimensions of the rooms? People will be able to give much better advice with that info.