IMO you need an interior designer If you do not use the DR why keep itbut I would need an actual floor plan to scale with all spaces marked with measurements. I don’t even know where the “keeping” room is

your photos aren't loading. houzz has gone down the tubes the last month. who knows what they're doing, but photos have a hard time uploading. try resizing it, and put them here in comments.

Option 2: Put large table in "keeping room" where bay area/fireplace is located.

Keeping room is on far right (bay window/fireplace)

Keeping room is on the far end of this picture. Fireplace has been redone, colors/lights are all updated. Kitchen will be fully renovated, so don't focus on colors/cabinets, etc - just layout.

What is a keeping room??

Does the Family Room share a wall with the dining room? If so, I might grow the kitchen to incorporate the keeping room area (a table near the fireplalce...yummm. Improve access to outside as well? Double yum) and open FR to current dining room (French doors). Which could be used in a way that better works for your family NOW while still being a "formal dining room" if yours is a neighborhood where people still want that.

Whenever considering remodeling I always keep in mind the impact on resale potential. Does what your doing add value to the home and make it more attractive to potential buyers? I feel this important because your home is likely your most expensive asset. Even though you don’t plan on selling or moving now, things can change... With that said how you live and use your home is also important. If the homes floor plan doesn’t match the needs of the occupants then something needs to change. Without knowing you and your family I think it makes sense to expand the kitchen island and move the casual dining table over in the “ keeping room”. There is probably also room for a couple of occasional chairs. I think keeping the formal dining room where it is important. Good luck, I hope this helps!

If you lose the wall between the kitchen and family room, where your range is, then you would have a large vent fan over the range and lose a lot of storage like you said.

However, if you made the keeping room an expanded area of your kitchen, you could always add storage there and put your table in front of the fireplace and have a larger island. If you have the budget, I'd be inclined to close the door to the outside up and put sliding patio doors on the wall where the double hung windows are now (on the left in the keeping room where the bump out is). You can remove the cabinet to the right of the pantry on your diagram and make a giant pantry (what we call the "Costco" pantry in our house).

If you never use the formal dining room (and you wouldn't need one if you make the keeping room the "dining" room), then you can always use it as a playroom or study or bonus room for kids. We used our formal dining room as the kids' playroom when they were little and now it's more of a study. My daughter's desk is in there along with a recliner and we have 3 walls of cubbies to keep board games and books, We used to have 2 desks along the one wall until my son decided to move his desk to his room; now it's just the one desk and the recliner. A friend of mine made hers a game room for her kids where they have another tv and gaming systems. That way the kids don't monopolize the tv in their family room.