On he up hill side, gear down and keep you RPM's up. Down hill I will drop my speed about 10 MPH at top of hill and drop down a gear or 2 as required to let engine help control descent. If speed gets to high, I apply brakes HARD to drop maybe 5 MPH below speed limit. This will let brakes cool if you need them again. NEVER ride you brake.
Have traveled 30K in last 7 years all over the West mountains,and even Virginia and West Virginia mountains and never had a problem.
I have a 5th wheel and use a 40+ year old Hydraulic brake controller. But with a bumper pull I would recommend a good sway control. You can probably find more information on sway control and brake controllers In the RV net.