Hi. We just finished our Alaska trip one week ago, left Western PA June 3 in our Class C. We obviously spent more time traveling than you are planning, but that doesn't matter. What matters is your trip and your time.
A couple of things to note that I didn't see posted yet. If you are still considering a ferry, plan to make reservations no later than the first week of March. I think you may have ruled this option out. If you think you may be going to Denali, make your reservations by mid-March. We were nearly closed out of some of the bus trips into the park when we made our reservations in March.
Plan on a couple of days of traffic not moving if an emergency. For example, a couple of days after we passed through Ft. Nelson, the Alaska highway was closed near Ft. Nelson for two days (I think) because of a wildfire. There are really no alternative routes around to use. You will be stuck. Make sure you have enough food and water on board for all "just in case".
Our Class C is 27 feet long. We did not tow, did not miss towing, and were able to go and park where we wanted. If you choose to tow with a Class C, based on a newer Ford E450 chassis the GCWR is 20,000 pounds.
If you are thinking of driving down the Kenai Peninsula to Seward, Homer, Kenai, or other towns, be advised the traffic increases on weekends as the Kenai is a destination for Alaskans as well. Just know that this happens and plan your travels accordingly.
The road between appropriately named Destruction Bay and the Alaska border is pure evil, pure and simple. You will be lucky to make 25 mph on a "good" portion of that segment. We encountered truckers coming in the other direction showering us with stones, easily driving well over the speed limit. All you can do is stay far to the right and slow/stop. I have the stone chips in my windshield and a few dents in the coach body as a fond memory.
There are many beautiful sights to behold in Canada and Alaska to make the trip worthwhile. Our family enjoyed the trip greatly. I hope your family will enjoy it as well.