Hello..I'm not sure what you mean when you say
"right rear brake calipers pick-up."
If you have power brakes with a brake booster, vacuum decreases in the power booster as the throttle opens. If you have a hydra boost system, the power steering pump provides the power assist. All system components (master cylinder, power steering pump or booster, power brakes proportioning valve, lines and fittings, calipers and pads and emergency brake) all need to be in good condition with no leakage or out of spec adjustments... to perform properly.
As you are loosing power while under heavy load uphill I would first check to confirm none of the brake calipers are hanging up (lift each wheel and check for free travel..no drag with brakes and emergency brake off)
The exhaust systems ability to flow freely is also critical. A plugged up exhaust system will not allow the free flow of exhaust gasses and severely limit the available power output of the engine...like driving with the choke plate closed.
Check here for more information about brake bleeding:
RV Net Open Roads Forum info Chevy P30 hydro boost brake power sterring...