On a big hill downshift BEFORE starting down, not midway. You shouldn't have to brake but a few times to slow it even further.
You won't have any problems with huge mountains with your motorhome.
You definitely don't need a dehumidifier in the West. :)
I don't know your planned route and what you want to see before getting to the major parks.
We like secondary roads but if you work your way to I-80 into Wyoming and get off at Exit 111 at Rock Springs, you would take Hwy 191 into Jackson, WY and Grand Teton Nat'l Park - no big hills on this route. You can then drive right into Yellowstone. Since you have a 43' you'll probably want to stay in West Yellowstone to tour Yellowstone.
When ready to leave Yellowstone, take Hwy 191 north into Montana. Then depending if you want to stay on the west or east side of Glacier you can take 287/89 to the east side or 83 toward Columbia Falls.
When you have your exact route planned out come back and ask about specific areas for RV parks.