I don't drive an RV much less towing another vehicle but I can't imagine why you're app is rerouting you, maybe it thinks its still closed for winter? The icefield parkway is a very well maintained proper paved highway and RV's are everywhere, like the plague! The tour buses have no issue either. Just stop for gas at Saskatchewan Crossing which specifically caters for RV's.
To tour the Rockies and not drive the icefield parkway would be criminal.
Saskatchewan Crossing - the only gas station after Lake Louise
https://www.thecrossingresort.com/features/rv-services
More info:
Alberta Road Conditions:
https://511.alberta.ca/#:Alerts