Regarding Tetons, how about the AAC Climber's Ranch? From what I remember, some of the cabins there take 4 people, some 6. If you call them in advance, they might be able to reserve a whole cabin for you and your family. Just a thought...

Not a question of politeness, shouldn't broadcast on the net but thanks; but you should know its family, not me, that own a GROUP Guest Ranch 1.5 hours NE of me.

The Climbers Ranch can be a great place. It's a truly spectacular setting with world class hiking right out your cabin door. However remember it's a hostel so you might not get your own half a cabin or the one little 4 bunk cabin. They're great people and will do everything they can for you. Be CERTAIN those little girls don't go near Cottonwood Creek or anywhere else any distance from the cabin, common area, and their nice little library

Well OP I understand your love affair with Montana, there's some great country up there. But remember that despite deceptive marketing the vast majority of Yellowstone and the Beartooth Highway is here in Wyoming.

Keep Wyoming clean, dump your trash in Montana. Heeh. Heeh.

In all seriousness have a great time up there.

I'm a teacher and I spent practically all of the 2014 summer in Montana and Wyoming, I'd definitely agree with the idea to pick one place and focus there. I'd lean towards Yellowstone with kids along. I'm guessing the kids will get a kick out of seeing animals and Yellowstone is the place to go for that. Seeing buffalo, Elk, Pronghorn and deer is a no brainer. If you stay a week and look in the right places you'll probably see bears and wolves.
If seeing animals is your goal check Yellowstone.net forums and invest in a good spotting scope with at least 30x magnification and a solid stand. Some people spend $800 or more but you don't need too. I bought a $75 scope and a $80 stand. Not as good as some but it worked. The stand was adjustable so I could put it down lower and let kids look through it. Another benefit of staying in Yellowstone longer is you'll meet more wildlife watchers and get a better feel for where animals are active and were too go.
One thought, are you just driving the RV? Driving those place in an RV would be a pain, often there will be an animal sighted near a road and the RV folks can't find a place to park so they have to go on. I might consider a tent or trailer since you'll be driving somewhere almost every day.

Well best of luck, if you do end up going to YNP send me a PM and I might see you guys out there.

Thanks again for all the wonderful input! In fact, after much research and pouring over maps and guidebooks, I have indeed decided to focus on JUST Yellowstone and Grand Teton for the two weeks we'll be in that area. Yellowstone just has so much to see, and couple that with Grand Teton's list of enviable destinations, and it seems like the best thing to do!

As for transportation, I've decided against to just rent a car and/or minivan, and I'm going to pack some essential camping stuff I can fit in our suitcases (sleeping bags, etc.), and then just buy some cheaper stuff when getting to Montana. I looked into renting a travel camper, but it's almost equal to the amount of staying in hotels/motels, which makes the cost even less desirable. This way we'll be able to split time between hotels and camping a little more efficiently, and depending on weather, we'll have some options.

Thanks again, and if anything else comes to mind, LEMME KNOW!

Gusto

Sounds like you have a solid plan. You could probably rent a tent at the REI in Bozeman.
Camping in Gros Ventre is good as was already mentioned. Get a good map of the area. If you end up with no open campsites there are a few places you can drive too that have dispersed camping. There are showers and laundry in several places but I usually went to Colter Bay (I think it was somewhere up there).

Place too see...

-If snow isn't too high there is a fire tower on the Beartooth Highway you can drive too. I don't remember exactly where but it shouldn't be that hard to find. The view from the top is pretty cool, you can also hike up the ridge (above treeline) and get some great views of the Absarokas. I'd combine that with an evening watching for wolves and grizzlies in the Lamar Valley. Its a great place but you'll want a spotting scope.
-Farther south the Hayden Valley can be a great place to see wolves, last summer didn't seem as active as 2013 but I did see wolves and lots of grizzlies.
-I've seen grizzlies fairly often on the stretch of road south of Swan Lakes (south of Mammoth Hot Springs). .
-Last summer lots of black bears were seen along the road near Roosevelt Lodge.
-Grizzly sightings seemed to be pretty common near the Jackson Lake dam last year.

I keep my camera binoculars and scope very close by in the car. You never know when you'll see something and you may not have much time to set up before its gone. Also I keep the bear spray handy, not just for me, I don't know if some other idiot will create a problem.