Kentucky bluegrass, and really just about any turfgrass, does best in sunny conditions. Therefore, trees and the resulting shade present a problem.

I also see you're in FL. That also presents a problem. Bluegrass is a cool season grass. In temperate climates, this grass is a superstar in the spring and fall but is kind of a dud with the heat of summer. In someplace like FL, bluegrass will probably not perform well.

I'm in KY and the University of Kentucky has an excellent publication on trees and turf: http://www2.ca.uky.edu/agcomm/pubs/id/id203/id203.pdf

Here's another discussion of pros and cons of turfgrasses, remember this is from KY: http://www2.ca.uky.edu/agcomm/pubs/AGR/AGR52/AGR52.pdf

Hope this helps.