I vote for hardwood or engineered wood through the whole space, including the kitchen. Opening the wall would be nice, but I suspect your appliances are arrayed along that wall? I'd paint the wall the same pale color as the living space, and hang a really big mirror on the wall if you can't open it. Then you open the wall visually, and reflect the light from the sliders back into the space. (I know...me and mirrors. They are great manipulators of space, particularly when you commit to making them big!)

For an instant lightener, paint under the chair rails in both rooms the same white you already have on trim and ceiling. Paint out the dark burgundy with more of the light yellow. Then change the interior part of your LR ceiling to a pale pale blue version of the blue/green in your paisley chair fabric. All the curtains need to go. Replace them with fiber shades and flank each window area with drapery panels that do not close, hung floor to ceiling. I think all three lamps are too petite and too Hobby Lobby. Start shopping for new ones, along with a new sofa more in line with the sleek style of your two slipper chairs. Keep your eye open for a stylish fabric to reupholster the dining chairs.

I would wonder first if I wanted to match the white paint as in the kitchen (white?) also, if I love the wood of the kitchen cabinets and hardware to be able to keep a uniform base for the rest of the home. You have white trim, okay, great start to be able to open the space up. Rugs: runner at the entry, at least a 8x10 in the living area, and at least a 5x7 for the dining area. How about coordinating curtains for this space. Is the dining room a sliding door? Because the hanging blinds in the livingroom suit more a sliding door spot. Rather have blinds or shades paired with curtains if both just windows. Rods and knobs in a coordinating finish as the kitchen knobs. The round table in the rectangular dining space seems off. Would love to sneak a peak at your lighting fixtures. Your entry table setup looks nice, what is your style, the table in the dining space seems cottage, the sofas heavy, could we get more of a view of the other corner of the fireplace? How about a curio on long wall in dining area. A table with a bench on the kitchen side would be nice.

Yes, I agree to have the sofa facing the fireplace and flank the fireplace with the chairs. IMO the only thing that is really not working here is the coffee table, it doesn't seem to have enough weight with the glass top and open bottom. and ottoman with a tray might be nice in front of the fireplace. I feel like the dining room could have a buffet to cozy it up a bit. I think you would need a pretty large rug, which might overwhelm but it could be a great way to tie it into the adjoining space. Over the fireplace, you need to put art, something that ties to the large piece that is in the dining room that will also bring cohesion to the space. You could put that mirror over the cabinet you have in the dining room on the short wall. Maybe you could try the rug from the living room in the dining room just to see if you like a rug in there...