There's two ways to get to Cranbrook from Glacier.
If you are on the east side of the Park, I'd highly recommend traveling from Browning to Babb on Hwy 464 (Duck Lake Road) instead of Hwy 89. From Babb, take 89 to the border and then into Canada either via the Carway or Chief Mountain crossings. Hook up with Highway 3 through Fernie to Cranbrook. Chief Mountain will take you into Waterton National Park.
The other way is to go through Whitefish and up Hwy 93 into Canada via the Eureka (Roosville) crossing. Hook up with Hwy 3 again into Cranbrook.
We've done all of those roads with no issues. Hwy 3 through the Crowsnest pass east of Fernie can be slow because of all the small towns and traffic, but isn't a bad way to go. It will take quite a bit longer than the other way through Whitefish.
While you are in Glacier, make sure to drive the Going-To-The Sun Road. You can not take your trailer on this road, but it is a great drive.
Sounds like a great trip. The fall can be some of the best times to see the mountains as the weather can still be good and there are far fewer people. The nights will tend to be colder though.
Make sure you check the crossing times as you will be travelling in non-peak times. I know Chief Mountain has restricted hours after Labour Day.