It's nice if you have more than one person in the kitchen at a time (prepping, washing, etc.)

i'd skip it. it buys you a few steps but isn't free and puts a hole in your island, right where you would set grocery bags down to load into the fridge, and where you would unload the fridge to cook dinner (milk, veg, etc). and really who would want to sit in that seat, by the prep sink full of carrot peels.

I would skip the prep sink.

Oh oh. We've got a tie. I was thinking that moving the sink closer to the sink would give about 3.5 feet on either side for prep or setting things. But that would also put the sink about two steps away from the main sink, so may make it redundant. And with us, since we've not had one before, we won't really miss it if we don't have one. I appreciate the input. It's so helpful to have such quick and pertinent feedback. Thank you!

It is so not necessary to have that sink in your island.

Usually there's a need for a second sink in the island if the island is a barrier to the work triangle. In your case, you can easily move from refrigerator to sink to stove without going around the island so it's not really necessary. And as others have pointed out, it reduces the usable counter space on the island. On the other hand, if you regularly have 2 cooks in the kitchen it may be useful, but only if it's large enough. Those 12" x 12" bar sinks are so small that they are only useful to hold ice for drinks!

If you switch the fridge and wall ovens, there is no need for the prep sink. You would get stuff from fridge, wash in sink, cook on stove without criss crossing your kitchen.

I would skip it - You don't want the sinks "back to back" and the placement in your sketch is off as well. Need that counter space!