What a wonderful opportunity to fix all those pesky issues!

I would do this:

Get a counter depth fridge and move it all the way to the left so it's not interfering with the door.

Move a new stove as far to the right as possible in order to have even the narrowest counter to the left of the stove so that people walking in aren't walking right into cooking pots!

Leave sink and peninsula as is.

Another option would be to remove the peninsula and do an island and put your stove in the island (still move the fridge to the left or put a cabinet depth fridge where the stove is now. The island will be quite small I think but it's another way to go.

Good luck!

You should definitely get some counter to the left of your stove, and you can also get real corner base cabinets that will be fully usable even in that tight corner. I'd be tempted to move the fridge to where the stove is and put the stove on the long wall where the fridge is currently (but in the middle of that wall), with an over-the-range microwave hood above it (yielding more free counter). Also, check inside your soffits -- if there's nothing up there, you can probably go another 6-9 inches with your wall cabinets which will mean a lot of storage.

Lots of people have doors in their kitchens, and they can still be designed to work well for you. Talk to a kitchen designer for more ideas -- even the free ones at the big-box stores may give you options you didn't know existed.

Some of these are smaller than yours, some larger, but you get some visuals anyway...

Oren & Shawna-Lynn's Kitchen · More Info

Carine Glades Kitchen Renovation · More Info

Coates · More Info

Maybe even a counter-depth fridge and the stove on that same wall, making for better cabinets on the current range wall...

Eastport Victorian Kitchen · More Info

Would it be possible to close off the door in the dining area and move it to where the window is? then you could build your refrigerator into that area, eliminating the peninsula and move your stove over to the wall centered between the cabinets where the refrigerator is currently.