Going to tell you a bit about Glacier National Park. Just so you know my perspective ... we live less than half an hour from Glacier National Park. Yes, we are spoiled and, having a Golden Senior Pass, we sometimes run up there on a whim for an after dinner drive. Yes, in my opinion (with my bias) it is truly a bucket-list place to visit. Less commercial than Yosemite and more manageable and less crowded than Yellowstone but with every bit as much grandeur.
So, the most important thing to know about GNP is that the E/W route over Logan Pass (where the, arguably, 'best' visitor center is) often is open less than three months a year and, with some frequency, does not open until after Independence Day. Given the record breaking snow we have received this winter, I expect this may be one of those years. It simply takes weeks, once they are able to even begin, to get the narrow, Going to the Sun Road cleared.
Second, yes, there are very strict vehicular length restrictions for Going to the Sun Road. It is a narrow and spectacular two lane (built in the thirties) but filled with very distracted tourists. No RV's allowed and, though I drove our F250 up there a few times, I do not do that any more as I found it uncomfortably, too big. But, not to worry, even if you do not have a small toad. The best way to see GNP on the grand scale (by that I mean an overview excluding weeks of hiking) is by way of the red bus tours. http://www.glaciernationalparklodges.com/red-bus-tours. If you choose to ride these restored and fun old buses (that come equipped with fun-loving, microphone equipped, salty drivers and tour announcers, there is RV parking available (for the day) just outside the visitor center and Red Bus pick-up spot which is near the west entrance (Apgar Village).
Third, RV parking, especially for Class A's, can be quite limited on the west side. The only choice is Apgar Campground (no reservations) and it fills quickly. Get's harder and harder every summer. Locals call it combat camping. With our 40' Class A, we don't even try anymore until after kids go back to school. Your 38' will fit but the number of spaces is limited. Best option is midweek arrival. No hook-ups of any kind on the west side (not sure about east side). Generator hours at Apgar are 8-10, 12-2 and 5-7 (I think). Camping choices (in the park) are far greater on the east side. There is one campsite over there that (I hear) takes reservations. If you want to stay on the west side, there is a KOA and a San Suz Ed private RV park off site but near the west entrance. I've never tried either. Then there are several other private RV parks within half hour of West Entrance. Search Columbia Falls RV Parks ....
If I get some time later today, I will add some comments regarding routes and places to stay along the way as we have made the trip from here to VA many times.
If I can be of help in researching or answering questions for you, speak up!