2nd edit, to answer some of the excellent questions (I called Mom and asked her the questions - you're really making her think about things differently). Thank you, everyone for your great questions and suggestions! I realize that this kitchen is really constrained :( Let's assume that the budget is unlimited. They are ok with moving the stairs and they are ok with removing the wall between the kitchen and dining room. The dining room is not huge: I don't have dimensions, but they have a large table with 6 chairs and there is adequate space on the side to walk comfortably. Mom thinks they could only take about 1 foot of the dining room for the kitchen, but they are willing to do that. Let's assume for now that they are NOT willing to swap the kitchen with the dining room.

They definitely want eat-in space, and are hoping for 4 spaces. This is a big priority. Pantry space is not as much a priority (they store extra food in the basement, which is down the stairs, around the corner, then down another 1/2 flight of stairs - not ideal, but not too far). The garage is down the stairs and around the corner - this is where the groceries come in.

The range is vented now - kind of. There's a small fan up there, like a bathroom fan. I'm sure it's not to code. But there is ductwork that goes outside, although I'm not sure of the diameter of the ductwork. They never use the fan now because it is not at all effective.

Thanks again, everyone!

Below is my original post:

Help, please, with this challenging layout! My Mom and Dad have a tri-level house with stairs that take up part of the kitchen floorplan. This will be a total gut-remodel, and you can assume that anything can change except that they will not replace the bay window, but it happens to be at a typical table height. The wall with the sink is load-bearing. The master bedroom and bath is behind the half wall that the stairs go below (see the last picture), so I'm thinking that there must be a beam or something in there for support?

They have a lovely view of the Mississippi River out the bay windows, and they like to eat there, overlooking the river. They sit there a lot, reading the newspaper, drinking coffee, etc.

They prepare food from scratch for most meals, often making extra and freezing for later. They host family and friends at least once a month - my sister and her family of 4 live just down the street. They have a small garden and do a little canning. My Dad makes bread in the bread machine frequently, so it sits out on the counter.

One of their goals is to make it easier for both of them to work in the kitchen together.

They would really appreciate any advice and help you can offer, and I thank you as well!

Here's the current layout (my Dad measured and drew it):

Here are pictures of each wall, going clockwise around the layout, starting with the river view:

The opening is to the dining room:

The sink wall:

The stairs going down to the family room:

Editted to make it clear that this is a total remodel, and the brick arch will be removed.

If you have the width, An open shelf island might be nice as well as handy.

Is an eat-in kitchen a priority, or would they happily give that up to gain more prep space?

Thank you, everyone for your great questions and suggestions! I realize that this kitchen is really constrained :(

To answer your questions:
Unlimited budget
Eat-in space (for 4, hopefully) is a big priority
Pantry space is not a big priority
Not willing to swap dining room with kitchen
Willing to move stairs
Willing to remove the wall between the kitchen and dining room
Dining room is not huge. They could steal about 1 foot from the dining room
Groceries come in from the garage, which is down the stairs and around the corner
There is a tiny vent for the stove, like a bathroom vent. It is vented outside, but I don't know the diameter of the ductwork

Thanks again, everyone!