I have driven Hwy. 2 from the Upper Peninsula in Michigan to Washington state several different times. I find a 2-lane highway much more enjoyable and relaxed than the freeways, which I avoid whenever I can.
Three or 4 times we've used the US Hwy. 2 route from our home in Manitoba to Washington state on our way to BC. We sometimes dip up or down off #2 depending on things we want to see. We like exploring small towns and cities and it's good for that. It is well-maintained all the way across and in general a peaceful, 2-lane drive. We've had no issues towing a trailer and it is easy to pull over any time you want.
On our way back east from BC we usually take BC Hwy. #3, just north of the border. That highway will get you close to Waterton Lakes NP, the Canadian side of Glacier NP. It is mainly a two-lane as well and can get pretty busy on weekends but it sounds like you'll be through there mid-week so you should be fine. There are several lovely provincial campgrounds along the way.
At Waterton Lakes/Glacier you can go back down into the US and return the way you came or you can continue on Hwy.3 to Medicine Hat, AB and connect up to Hwy. #1, which is the Trans-Canada Hwy. As the name suggests, it will take you all the way across the country. It does not seem to be as busy to me as the US interstates but it is the main interprovincial route with lots of truck traffic.
One benefit of travelling through Canada is the extra value you get with your US dollars. I heard today that the Cdn. dollar is trading at $0.74 compared to the US dollar. It's been in that range for several years, only worth about 3/4 as much as yours. True, our gas may be more expensive but may actually even out when bought with US dollars.
After Medicine Hat we usually dip down to Saskatchewan Hwy. 13 and continue east on it to our home in Winnipeg. It's an especially quite highway sometimes referred to as the
Ghost Town Trail. If you like exploring ghost towns you will find many along this route. You pass through wonderful grasslands, similar to the northern states, but far less populated, and can visit Grasslands NP if you like. Cypress Hills Interprovincial Park is an oasis of forest in the grasslands and is also wonderful to visit.
If you're still in Canada east of Winnipeg you get into heavy rocks and forest that extend nearly to Lake Superior. At the Manitoba/Ontario border the Trans-Canada Hwy. becomes a two-lane again until you come to the major centres in Ontario. That too is a wonderfully scenic trip. At any time it's only and hour or two south to the US if you prefer.
I hope that helps.