It has many years since I drove US 2 to Glacier National Park. The scenery on US 2 and I-94 are the same across North Dakota except I-94 goes through Teddy Roosevelt National Park with a pretty view of the North Dakota badlands. A big disadvantage to US 2 was the numerous towns that required dropping down to 25 mph back when I traveled that route. It may be different today but I found I-94 a better choice.
You may want to consider taking I-94 across North Dakota and then go north on 200S, just west of Glendive, MT, to US 2 and on to Glacier National Park.
As mentioned, you can't take a big RV on Going to the Sun road but here are tour buses, etc., that are available. You don't want to miss this extraordinarily pretty highway.
2015 Wildcat 282 RKX
2011 F350 Lariat, 6.7 L. Diesel, 8 ft., SRW, Reese R20