If you add a rug to the seating area it will need to be as wide as the one in the dining area and extend at least a foot past the credenza/bar. Tape that out with painter's tape and see what you think. If you add a pair of armless chairs facing the sofa, they will need to have at least their front feet on the rug as well. Consider a backless settee instead. It will divide and define the two areas yet not interrupt the flow between them. The front windows have room for curtains to be hung properly, but the back windows do not.

Thank you for your suggestions decoenthusiaste. You mentioned the size of the rug in your suggestion, however, I'm still left wondering if I would put a solid print or patterned print rug? I love the idea of a satee! What alternative window covering could I use for my back window since there isn't enough space to hang drapes properly?

You'll have to decide on the rug when you see what's available in your required size that still works with the larger rug in the DR. Have you checked to see if that company makes the same rug in a smaller size? That might work. That appears to be a slider in the back. You could match the front drapes with a cornice or faux roman all the way across the top.

While you don't have as much wall space on either side of the of the window, there is enough room for stationary side panels.
Just mount the rod high as you did in the LR.

Backless seating is a great idea!

Here is one of our designs; notice how the 2 chairs here divide the space? You might not need two rugs, just a way to make the spaces into a dining room and sitting room.