I've done that route in several rigs, towing a two-axle mutant-carrying trailer that weighs around 9000.
I've pulled that trailer with motorhomes and several trucks.
DEFINITELY go out on the freeway with the RV and trailer (with something in it that gets the weight up to where it'll be on the trip) and see how it drives first!
One year I had mine behind a motorhome, shorter than yours, but with a heavy-model EZ Loader weight-distributing hitch cranked as hard as it would go, and it drove so bad I had to turn it around and go get something else.
Your 34 footer will have that long overhang, about 8 to 10 feet from the rear axle to the hitch ball but it ought to have enough wheelbase to do OK. However you really really should have a weight-distributing hitch and crank it tight.
The route itself: I always approach from Alturas because I'm coming from north, whether it makes sense logistically for you I dunno... but, the climb from Cedarville is pretty steep.
Heat is what kills rigs there. I've been on the side of the road there a few times, either due to my own rig or a friend's.
I'm assuming "older 34-foot motorhome" means it's either got either a Dodge 440 motor/727 transmission if it's about 1977 or older, or Chevy 454 motor/TH400 trans if it's about 1978 or newer. That's the same stuff in a 3/4 ton pickup, you'll be working it REAL hard.
DO make sure you have a good, big transmission cooler. Maybe put in a second one. Add an electric fan to your radiator. You'll be making a lot of heat but going too slowly to get enough airflow.
DON'T hold your foot on the floor and strain the thing as hard as possible climbing that pass. Shift into FIRST, let up on the gas, and walk it up. You don't want to get there first, you want to get there at all. Don't floor the gas going up the pass with a heavy trailer. I've personally blown up motorhomes doing that, even WITH a new trans and big coolers.
I won't do the pass in anything with an automatic transmission without yanking it out first and getting it rebuilt, unless I KNOW it's pretty fresh. I also don't go without a new radiator, unless I KNOW it's pretty fresh. Trust me, it's cheaper and easier than blowing it up on the pass. I know all about it, from many times on that drive with my own and my friend's rigs.
Get a good brake controller, like a Prodigy. Make sure that older motorhome does not have one of those older brake controllers that simply turns the trailer brakes "on" or "off". Coming down the other side is kinda' gnarly in a heavy rig with an automatic trans too! Again, you gotta shift WAY down and slow WAY down and walk it down. I've been careful but friends of mine who didn't listen and got impatient behind me have cooked their brakes coming down the pass.
It's doable, I always go that way, all I'm saying is set yourself up for it and take it easy on the rig.
Oh, one other thing about road-testing prior to the trip: You must have the trailer hooked to it, and loaded as heavy as it will be on the real trip. Several times I've road tested trucks for the trip and they seemed fine, the problems don't show up until you load them HEAVY.
Too much is not enough, and when in doubt double it.