As you stated in your notes, you know what is working and what is not. Taken as a whole, since the space is so open, it is neccessary to unify the entire area. Right now the balance is off in part due to the white sofa, on one end and the cherry mid tone cabinets on the other, weighing the kitchen side down. Honestly though primary issue is the flooring. The best solution would be to have the spaces in the same flooring material. If at all possible I would replace the tile with matching wood. The cherry cabs with the oak floor would be great. Wood floors in kitchens have been used for ages.
The break in the flooring is in a very awkward place, creating what appears to be a "no-mans land" between the island and the beginning of the wood. I realize this option may be completely out of the range of possibilities, but it is a primary issue. DO NOT FRET however, it can be overcome with the strategic use of paint, accessories etc.
I don't get any feel of a focal point, with the exception of the kitchen, again due to the cherry cabinets. The fireplace, commonly used as a focal point is in a bit of an odd location visually, but from a functional standpoint it would serve to warm the entire space as it is centrally located. I do think it should be played up more, as it seems an after thought right now. The seating group is also lost as the white sectional disappears against the white walls. All can be corrected with a new wall color common to the kitchen and breakfast nook, some accent paint on the fireplace, and mantle, and a larger bolder rug thrown on a diagonal create intimacy and emphasis. I would also add a bold rug in the breakfast nook under the table to define the space as separate from "no-mans land"
You have a wonderful rhythm established by the windows, but you are not playing it up as you could. Add some window treatments to the ceiling to give some lift to the rooms, and it will also add some vertical stopping points as your eyes roam around the room. The vertical is also needed due to the overall horizontal layout of the rooms themselves. I love the idea of a mirror over the fireplace, but it should be one very large one.
The furnishings you do have are ok, just need some tweaking, and as you say you need different art, and some unifying accessories, etc. Although I don't like the barstools, there are way better choices at any price point. I would stay away from blue and rose as it feels dated (I know you say the fireplace tile is rosie, and depending on how rose it is you might want to rethink it). Apologies if it is your favorite combo, but it's my job to be honest. I definitely think a single color on all the kitchen, breakfast, and family room walls is the best way to tie it all together. Treat the fireplace and the walls on each side, and above the mantle as an architectural element and do them in an accent color, with another accent on the mantle and surround. The brass screen is way too strong and bright, and seems foreign to the space, as the other metals appear to be bronzes, with copper accents? Hard to tell in the photo.
I can certainly help you out with specific paint color selection, overall color palette, accessory ideas, rugs, etc. if you would like, simply make your selection from the virtual designer menu. Hopefully this review will give you a good starting place to begin unifying the rooms.
Thank you for the opportunity to share my ideas with you, and I hope to work with you further.