We've taken HY 2 several times from Glacier National Park to Bonner's Ferry, ID; and also to Priest Lake, ID. It's fine-- a very scenic route, and it avoids Lookout Pass on I-90.
Given our location in the midst of your route, we haven't done the entire trip in one outing, but we've done HY 3, to Alberta, which is fine. From the Creston Valley, we frequently drive BC highway 21 (off HY 3) to the border crossing at Porthill (small and usually fast and pleasant,) which becomes ID HY 1, which turns into HY 95 and 2 (again,) This gets you to Coeur d'Alene, and from there you can go westbound a short distance on I-90.to Post Falls.
From Calgary, it might be just as easy to cross the border at Kingsgate, south of Cranbrook, BC on HY 95.
It should be a pleasant trip in the summer, with lots to do along the way if you have time for it. There are some beautiful lakes at Sandpoint, ID and Coeur d'Alene.