"It's the Alcan to those of use who have been in Alaska for a long time.
Bill"
^^^^ Bingo. That's how it was referred to in '74 and the name stuck with me anyway.
The proposed trip is too many stops and not enough days. Suggest (as others have said) doing the Western U.S. on another trip and keeping the focus on Alaska / Y.T. / BC / Alberta this trip.
The Alaska portion of the trip seems (granted, I live in Los Anchorage) to put too much time in Anchorage, unless the intent is to do stuff that involves going to i.e. Palmer, Glennallen or Seward, but those are already on your list. You might want to put some time in for the Kenai Peninsula (Slodotna, Kenai, etc) or Talkeetna instead of 10 days in Anchorage.
Weather can obscure the mountaintops, particularly Denali, but (except for June of this year), one won't escape rain in Alaska, so that should not be a go / no-go factor.
Alaska and Western Canada are great for driving and sightseeing...but I'd suggest that some thought be put into what else you might want to do (fishing, flightseeing, boat trip, glacier hikes, camping (away from pavement), hiking, etc) and slot in some days for those activities. Although it's hard to predict, some of the "tourist" activities tend to book up well in advance and that may end up being the critical path for your trip.