Here is a route I like to take....
Take Highway 2 from Spokane to Newport, WA and continue on to Sandpoint, ID. Then take Highway 200 east, going around Lake Pend Oreille, through Hope and Clark Fork, ID. Once into the state of Montana a few miles turn north on Highway 56 (Bull Lake Road), which will take you into the heart of the Cabinet Mountains in western Montana. After 35 miles you will join up again with Highway 2. Turn right and go east on Highway 2 and travel along the Kootenai Fork River and into Libby, MT and then into Kalispell and up to the West Glacier/Apgar entrance to the Park. Stay on Highway 2 if you are traveling on to East Glacier and Two Medicine area. This route I outlined is very scenic and quite enjoyable, in my opinion.
This route will take a bit longer of drive time, but I prefer it over the I-90/St. Regis/Plains/Elmo/Kalispell route. It's only about an hour quicker to go I-90 and St. Regis, but not near as scenic, in my opinion. I understand if time is a concern and very tight then by all means take the quicker route. But if you can spare an extra hour then go down Bull Lake Road. You won't regret it. The entire way is all paved and you can travel normal highway speeds (i.e. no gravel roads) on all the highways between Kalispell, Libby, Bull Lake, Sandpoint, Newport, and Spokane.
Have fun, enjoy the views and be travel safely!!
The worst bankrupt is the person who has lost his enthusiasm.