You are not allowed to take any vehicle more than 7' wide over the Going to the Sun road, perhaps your tow car, or there are several tour services that take people to the various rest areas, and then pick them up on the next bus to take them to the next stop, and back to your campground at the bottom of the hill, either the east or west sides.
I did take the alternate route to from the west campground towards Yellowstone back in 1994, I did not recall anything significant about that drive, but I was used to driving through steep mountains back then.
How many miles are you planning on driving, and how many weeks? That does seem like a really long trip. I recall hearing about a 5000 mile trip that a friend took, and they never really stopped to do more than take pictures! You do not want it to all be 800 mile travel days, and I would suggest skipping Glacier NP, unless you are going all summer! It is just more cliffs and rocks to look at, that said I did go there in 1994 and back in 2006 while on my way someplace else.
Fred.
