I found this photo online, perhaps it will help. In this picture the crown molding on the cabinets flow from the kitchen to the adjoining room. Maintaining continuity with the color and some of the trim detail will make the rooms transition nicely. Don't overlook the details like hardware finish, lighting and plumbing fixtures as these elements can also tie the two styles together. I hope this was helpful.

Try wood and glass. Consider hanging the mirror vertically and about 5" from the sideboard top. You could also move the table under the light fixture, change it out for a chandelier, and put the sideboard and mirror on the clock wall where the mirror could double the chandy which should hang 36" or less above the table top.

Love your style and you've got some beautiful furniture there! A deep aubergine purple velvet on your wingbacks would look stunning. I'd tend to stick to purples in this area to keep it classy. Also, a dark purple would be more practical with kids than a cream. I'd keep the chairs you've got, unless they are really wobbly. Get someone to check them out and give you a quote for repairs and then you'll have a price to work against to see if you can get cheaper. OnePlan is right on the style and yet I don't think they look out of place in the room. I also like the idea of bench seats or if you wanted something really different, you could get a church pew?! I don't think the room has too much dark furniture as it is a large light area. Keep us posted with pics/samples of possible fabrics you find. Also, check out fabric outlet places.

You can of course have a furniture repair business add material and refinish. Or you can add a center accent piece of tile, or wood inlay. If you're going from a narrow rectangle to a square, you would need to disassemble the table anyway, might as well do something fun with it.