Sorry about the sideways images, they are iPhone images that I oriented correctly on my computer before I uploaded :(

What do you find awkward with the current arrangement?

Well, disclaimer, I'm no pro, for sure, but, if I'm understanding how things are laid out, it seems that you can take the current stair space back and add it to the square footage of the kitchen. You then, leaving enough room to step into the house, move the short stairs over in front of the door, having them start as comfortably close to the open door as possible, and then coming up, running parallel to the back wall. Perhaps you would have room for just a short landing, where you would turn and come into the kitchen, and maybe you could hang some hooks there for coats, small bench to put shoes under, etc.
I'm just taking a shot here, but it does seem to be the best way to re-configure the stairs, although I'm not sure if you'd have enough room to do anything but step off the stairs, turn, and walk into the rest of the kitchen. Having the stairs coming up at the very end of the room does seem to be the best way to get extra room, to me-at least from what I can see in the photos.

We are considering a significant remodel here however my husband (who would do the build work) is dead set against me hiring a kitchen designer because "it's your kitchen why would you have some one else tell you how to use it?" It's not a huge space which makes me think it's trickier, not easier, to redesign.
@ppf. most of the back wall of the kitchen is the stair well, and as such useless for kitchen use. The fridge area is on that same back wall, past the stair well, nearly into the dining room which means there is no work triangle at all. In the last photo, the fridge spot has the damaged floor which is right on the edge of the dining room.
@lucindalane I'm trying to envision your suggestion. I think you mean that you would come up from the door straight ahead into the kitchen but how do you get downstairs?

Still unsure of your dilemma. If you want help with a kitchen design, post a floor plan with dimensions. It's really difficult trying to understand a bunch of pictures and how everything relates in the space. Be sure to write big so we can see, and include a bit of the surrounding rooms so we may understand how the kitchen fits into the house.

If you are seriously considering moving the stairs outside and closing in the rest of the space, you need professional assistance. This is a major remodel.

Build a knee wall in lieu of the wrought iron railing.

This needs pro.

Agree with need for floorplan, but my first thought is that if you remove the iron railing and replace it with a half-height wall, then you can install an entire row of base cabinets along that side with a counter on top and maybe even a breakfast bar, if so inclined (based on the fact that a table used to fit there). That would be a lot more storage and would keep the back door from being so central in your kitchen.

A kitchen planner is never a waste -- they can help you fill the space with functionality, pick the right cabinets, and come up with ideas you didn't even know were options. Better yet, at places like Lowes, they don't charge for their services, so what's the risk? (You do need to come in with careful measurements of everything you have and at least a few ideas of what you want to add, and photos of current cabinets, if you want to add not replace, are also helpful.)

I agree that a kitchen planer or designer is not a waste, especially with your challenging project. I good designer will not talk you into anything you don't want, rather will take all your ideas and wishes and make them work within your space and budget.

Sorry, I guess I somehow just "read" over the part where you mentioned the stairs. Is it feasible to build a wall where the railing is now? That would give you more space, and also be a safer barrier. You would, of course, then need some good lighting for the stairs, and the whole area, but you wouldn't have to worry about moving the door or any of the stairs.