The room is too small and chopped up to accommodate both living and dining activities. Maybe the large storage room off the kitchen could be removed and converted into a dining area. In the living room, the corner fireplace is taking up a lot of room. Can that be removed as well? If so, you'd have more room for seating in that corner.

Is the wall between the kitchen and family room a full wall or a bar? Hard for me to see.

Are you able to provide room dimensions? Consider replacing the hinged patio doors with a slider to eliminate conflicts in the family room. What is their primary focus - dining, entertaining, both? Identify that, then work on the layout. I agree with the idea to repurpose the storage room (some or all?)
for dining. If storage is needed, is there room for a small banquette or small drop leaf dining table along the right wall (adjacent to the stairs) in the FR? Europeans typically make great use of small, combined use spaces. Search for inspiration there.

auntthelma - It appears to be a solid wall to enclose the mechanical room between the kitchen and family room.

Thanks for the responses! Unfortunately, I don't have the room dimensions. We're limited in what we can do with the existing space. The space between the kitchen and family room has 3 heating units and the storage area houses HVAC, and it's too expensive to redo/move. The existing space is currently the laundry/storage room that we are converting to a kitchen so my parents can have their own in-law suite. The only change we can really make is the entry way from the stairs on the right. We have the patio doors as French doors because that's their entrance/exit and we need something they can lock when leaving.