Last August 2013 we had planned for 3 to 4 nights in Glacier NP but ended up spending 14 nights in and near the park. The weather is often cold, damp, and rainy in August, but the weather was awesome with ideal temps & sunny so we adjusted our trip around the change. Ten of our nights were spent at the east side Rising Sun campground which did not require reservations. They did have a 10 night limit, I recall $20 per night for us non-seniors. Seniors was much less, maybe $10 per night, but not 100% sure on how cheap. No hookups, just a dump station at the campground entrance. That campground is maybe 5 miles inside the park from the Saint Mary's east entrance. We had family stay one night in the KOA outside of Saint Mary's. Our Rising Sun campsite was so much nicer....really SOOO much nicer. We would have been miserable in that KOA, but understandably would be different if we needed hookups. The bus picks you up at two locations near Rising Sun campground, one by the Rising Sun Lodge. Our particular campsite happened to be a lot closer to the Saint Mary's Lake boat dock to the south so we walked there to get on the bus.
Wi-Fi is available at the Rising Sun lodge restaurant. It requires a password so just ask the restaurant host for it. Cell service is nil to sketchy, so Wi-Fi became essential for us to communicate with the outside world. We really enjoyed our meals at that restaurant with the hosts and waiters/waitresses, all made the experience better yet. There was a restaurant in the town 9 miles north of Saint Mary called "The Cattle Baron Supper Club", a good place for a great monstrous steak. It's right off Highway 89, west side of street.
Like you say, a 2350 is not permitted on the Going To-The-Sun Road. To drive your 2350 to the west side of the park, you will have to take the southern route around the park. Keep in mind that the land outside the park is National Forest so we took advantage, sleeping twice on those massive pull-offs, and once in the rest area along the route, (shshsh, officially no overnight parking in the rest area). The trains were loud those nights but strangely, we actually enjoyed that. It was one trip we decided to leave our Jeep Liberty home....oh well. It worked out okay, but the Jeep would have improved time efficiency a lot. The 2350 can be driven to all other places except one other scenic road in the south/east area of the park. I forget the name. Fortunately there is a longer way around so you can easily get everywhere around that region. Going To The Sun Road was the only real obstacle for us. I do believe a PC-2100 would be allowed to drive that road. If it is questionable, I would do it anyway for the buses on the east side are so much larger. The west road is more narrow with tighter hair-pin turns but a PC-2100 can handle it without any concern. I think the restriction has much to do with parking up top at the pass. If you can take up just one parking space, then you'll be fine.
When driving around the park east to west, be sure to visit the huge lodge there in the south/east. We got lucky and were well entertained buy a young couple singing and playing guitar. They were great. A violin player serenaded us at the Grinnell Glacier area lodge. Great affordable ice cream there too. Good restaurant food at all lodges. The west side area called Apgar by Lake McDonald is domesticated with accommodations of all sorts, which can get congested. It's all worth visiting, our favorite was all the east side, best at the Grinnell Glacier lodge area. There always is bear to be seen sometime in your day driving along the road there, or at the lodge itself, best at daybreak. We seen 4 different bear, some repeatedly. There was a yellow grizzly that hung out a couple hundred feet off the road for days of which always drew a huge roadside crowd. Never so close to run to your car. So beautiful a creature. Be sure you each have a pair of binoculars or you will be fighting for them.
I would call the park and ask if your dog can ride the bus with you. Be aware of dog restrictions on trails, I would assume there are.
If you are good all-day hikers, I have some tips for some grand day views. The hikes to Iceberg Lake and Grinnell Glacier Overlook were our top two. But there are many shorter hikes for a half-day and less to awesome views too.
This type of trip is typical for us of which our PC-2350 with all it's amenities and capacities serve us well. We just don't hook-up to much of anything except a fuel pump hose, and propane twice in the 4 weeks.