Sounds like you want 4" borders, to take a 30x48 quilt to 38x56. If you want to float 2" finished squares in the 4" finished border, you will need 1"(finished) on each side of the squares, so 1.5" strips. I would probably cut 2.5" strips of the main fabric, and 2" strips of the border fabric. Strip piece 2"- 2.5" - 2" and cut into 2.5" sections. Then cut border sections 4.5" x ? to go between those sections - depending how far apart you want your floating squares to be. 6" (6.5" cut) would work out pretty well - you'd get 3 floating squares top and bottom, 5 down each side, plus one in each corner.
I don't know if that makes any sense? Made a lot of sense in my head