When going up a mountain, when you feel your coach jumping in and out of gears, shift down one. Check your tacometer to make sure you're not over reving in the lower gear. Check your manual to find out what you should be tacing in each gear. You will probably have to slow down, but some of those gas engines can out pull my diesel rig...but only when I'm towing the jeep. LOL! And be sure and keep an eye on your heat gauge. If you start heating, drop a gear and slow down. Again, check your manual to see what max heat is for your rig.
Going down is trickier. Slow down to the speed you want to go down and gear down at least one gear before you start down. Watch your speed, when you've gained 5mph over what you want to come down, apply the brakes FIRMLY to slow back down to the speed you're comfortable with. Do not ride the brakes, you'll burn them out. You may have to drop another gear to stay where you want to without applying the brakes to often. Play it safe, go down at a lower speed than what you may think you're comfortable with until you get a feel for the coach, the road and your capabilities. Your first couple of mountains will be knuckle biters and you may have to change your knickers when you get to the bottom, but pretty soon you'll be comfortable doing it.
I most definitely would NOT take 89 into Prescott, and as much mountain driving as I've done, I would come back a different way even if it was further. It's a blast on a motorcycle, tho!! LOL! 17 to 69 is a much better route for an rv. IMHO.