With such a small space along that wall, you really can't get the dishwasher any closer to the sink. What is that, only about 4 feet? It is too close to the cooktop, too. Yikes. Moving plumbing is pricey. Perhaps you can live with it for now, until you move, OR can squeeze out some more space for a larger kitchen.

We are gutting the kitchen so I can play with the layout. It definitely doesn't work where it is at. We may bump the right wall out 2 feet to gain some more space, but then my window won't be centered. The kitchen is about 12.5 feet long by 9 ft. wide.

The floor plan you show has the stove under the window. Why not eliminate the right side of the kitchen if you are going for a total kitchen redesign? Add an island to replace some of the cabinets you loose when cutting off the right side. This way you will have room for the sink under the window & the DW to the right side. Does that make sense?

Windows can be moved if you are doing a full kitchen gut. I add 2 feet on the left side, 3 feet for the sink cab, then 2 feet for the dishwasher. This only adds up to 7 feet & you have 9 feet. Even w/ 2 or 4 inch spacers here & there you should have ample space w/o moving a window. Then you will have an opening in the wall to the dining room. Whoops, is that a fireplace?

Okay so you have an area of bare wall behind the fireplace & then plenty of space for a large opening to the room to the right (whatever the room is) and plenty of room for a healthy size island with an area facing into the kitchen for counter stools. Then another opening on the close side of the island to travel into the kitchen. Can you see it?

What this would do is open up the right wall of the kitchen for a free standing island for additional prep work & for counter stools, thus leaving the window where it is the sink where it is (a new farmhouse sink) & the DW to the right of the sink. And If you have plumbing in the basement under the island, add an additional vegie sink.