I love your outside entertaining area. It does need a color that would complement but give the area a focal point. I like the darker red,orange colors you may find in natural. You could dress up the table with accessories and place cushions in a complimentary color on the benches. Colored potting containers would also bring it all together. I like the uplighting here in the photo you could place along the back fence to add drama. Your area reminds me of Modern mediterranean landscaping.

After the worst drought in 30 years - good to get some rain. Loving the chandelier

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.

The blue is awesome (grey is too trendy)! The reason it stands out to you is perhaps because it's the only real colour there. Bring in the blue in a window treatment, a small appliance that sits on the counter, a pretty tray or area rug. Also, it is more appealing often if there are more than 2 colours - so right now you have a white and blue colour scheme - bring in red or orange or fushia - something from the other side of the spectrum (like you did with the yellow flowers but in a more permanent way)!