Draw a floor plan with measurements, doors etc for more useful help

See the floor plan in the imgur album.

Ok, here you go

Which wall (if any) is an exterior wall? What's behind the wall where the DW is currently located - garage? We're trying to place the range such that you will have a proper hood for venting. All else can be adjusted after we know that info.

Thank you, dishwasher wall is exterior wall that opens to air (kitchen floor is above ground by a floor). That's a good idea to put a vent there (would be cheaper since it's a short route).

Thanks, Gillian-- the island is tricky there because opposite the refrigerator short-wall is the sunroom, and on the left a sliding glass door to a deck. Maybe a small island?

Forgive the clutter -- I have a 2 year old and 1 year old and we both work. This picture is the rest of the room off of the peninsula (pictured). That wall next to the sliding glass door is 29" wide

"Something" has to be radically changed in order to make the expenditures worthwhile. ROI = return on investment = money / your labor / and your time, of which you have very little to spare. Suggest you post; photos of the whole space (dining/sunroom/etc) and measurements of same.

Agree that we could be more useful with more info. But to me, what jumps out is that terrible wasted space marked "false corner cabinet"! I think you could do as Patricia suggests and move the range where you have the sink -- then get rid of the spice pull-out and you could probably fit another lazy susan or other corner cabinet in that corner. The peninsula would fit a sink and dishwasher, and your drawers, etc., could be on the range side. If you stick with a 30" sink base, you might even be able to get a trash pull-out over there -- no idea where your trash is now.

With this space, I'd put a vented microwave over the stove, so that you free up more of your counter space. As long as you can get a short vent run, they do a decent job.

@acm The only exterior wall is behind the (currently located) DW. I agree with a micro over the range so as to conserve space.

Vented microwave ovens have insufficient air flow for serious cooking, and much too little for hot cooking (pan temperature at the smoke point of peanut oil, meat searing, etc.).