You will need to post some photos to get good advice.

So the cabinets are accessed from the 'outside' of the L shape?

I am trying to attach a drawing to show you my dilemma

Looks like a galley kitchen at the moment with an eating area.

I was about to say the exact same thing. Some people really like galley kitchens -- minimizes space kitchen takes up while still maximizing storage. Minimizes steps between important features of kitchen. But intended as one-man work area -- two people cd be stepping all over each other -- and definitely not the kind of fashionable kitchen we are seeing in so many photos! If you wanted to open it up a bit, couldn't you just move the sink to the other side of the DW, expanding that 3' space to 6'? If it were mine, I'd be inconvenienced by having stove on end, which led me to wonder if you really need both doors... What are you hoping to accomplish?

I always wanted an island but it just isn't possible if I want to maximize storage space. So I guess it is going to have to stay a peninsula but I want a place I ( and hubbie) can sit and eat. I thought I could push out the peninsula where the sink - or DW if I swap places with the sink - so there would be an overhang for two stools. There have been suggestions to put the sink in the nook underneath the kitchen taking away the peninsula - what do you think?

If you kept DW in same position but put sink on other side, space freed by sink cd be enough for bar stools on either side, right? But if you just "chopped off" the countertop at the DW instead, wouldn't you have room for a rectangular table with the short end toward the "front yard"? To keep it less crowded, you cd do one of those built-in benches with pretty cushions against the wall at the top of yr diagram, looks like you've got 5'9" between wall and door, then a couple of chairs for the other side. But why do that when you've got all that "breakfast room" space? Did you have some other use in mind for that space?

And if yr real purpose is to get an island, why not just chop the whole countertop off where the garage wall ends and put a rectangular island, again with short side facing "front yard," and relocate sink and DW to that (very minimal plumbing move)? Looks like you'd have an area about 9'x9'8" (which has to include walking-around room) so the island cd accommodate bar-stool seating also. My preference, though, wd be to get the stove into the island and if there weren't room for both that and the seating area, put a table for two in the front corner adjacent to garage, again using built-in benches to economize on space. Maybe I'm being dense or I read the measurements wrong, but couldn't this work?