First off, I am not familiar with your tractor, but am guessing it is an HST?
The brakes are on the right because the clutch (on just about every tractor I can think of)is on the left. Trust me, you do not want to try to hit a left brake and clutch at the same time with the same foot. I backed into my Uncle's pickup by doing that on a 9N Ford in about 1976, they had left brake and clutch on the left and the right brake on the right.
Just advance the hand throttle before you want to turn with the brakes. With my old Allis Chalmers WD I can turn around (either direction) and run the rear tire tracks over the old tracks. It has a hand throttle only. It also has an actual hand clutch for the transmission; allowing the PTO and hydraulics to continue operating, very handy for operating a rotobaler I am told. Its not quite independant hydraulics and PTO but it works pretty good for being designed in the 1940's.
Hope this made sense,
Robert