Yes, take your car. If it is high clearance and/or four-wheel drive even better. There are lots of places to explore in the car and not the motorhome.
The main advise I always give is not to be in a hurry, especially in the areas with bad roads. That sometimes means 20 to 25 mph (30-40kph). That reduces the chances of damage to your motorhome from rocks and frost heaves. Be ready to boondock, be prepared for long daylight hours.
Stock up on groceries in major towns, like Grand Prairie, Prince George, Anchorage, Soldotna and Fairbanks, the small places charge higher prices. Whitehorse is expensive but much cheaper than Watson Lake. A extra cooler to hold fridge items for a few days will be useful.
Be prepared for sticker shock on fuel in northern BC and Yukon.
Keep a camera ready.