Ted,
You are correct in that the same hydraulic pump powers the cooling fan and the power steering, and yes the pump pressure can be checked with the right equipment. You have to have a way to tee into the pressure hose to your steering gear for a pressure gauge that reads at least 2,000 PSI and have a snubber valve inline that can be closed to read maximum pressure. This arrangement will allow you to read the line pressure under all conditions and determine if low volume or low pressure is your issue.
There are several conditions that can be causing the condition that you are concerned about. I am not sure if the hydraulic pump on your coach is belt driven or if it is direct drive from the engine timing case. If it is belt driven, a slipping, worn, or improperly adjusted belt could be the cause. Other causes could be a defective pump, steering gear, or fan control (wax valve) that is that is diverting too much flow to the fan motor.
However, before you start chasing illusive issues, ask yourself how much the steering has changed. A stiffer steering feel while stopped is normal because it takes considerably more force to turn the front tires while stopped than it does when they are rolling and the hydraulic pump is operating at lower RPMs so the hydraulic force available is naturally reduced.
Gerald