I had a similar problem, Went through a lenghty process of checking over the front end found the left axle shaft ujoint dragging a bit when i turn the spindle left and right, i replaced it and the problem still continued but wasnt as bad, i decided to go with a ps pump as mine was original ( had 174,000 miles on it ) went with a napa reman with the filter option, that seem to solve the problem, then a couple of months later i noticed the same problem again, (hard steering when stopped and foot on brake pedal ) at this point i was about to lose my mind, My front end alignment shop advised me to check the air pressure in the tires only to find the fronts were at 55 psi i normally run 65, i adjusted the air pressure to 65 and so far so good.
I have also read were even the reman ps pumps can be low on pressure right out of the box. the dodge service manual describes how to test for correct flow and pressure on a ps pump/steer system,low ps pressure could cause this problem that your describing or possible problem with the hyd portion of the steer box.
If you need the ps specs let me know and i will look them up and post them, my truck is a 2000 cummins powered 3500,that i switched to a single wheel instead of the dually. Regards Rich