How much of the weight is in the car and how much would be in the motorhome? And how do you plan on moving your motorcycle around? I don't really see any particularly convenient way to do it offhand; it presumably won't fit in the car, and it presumably wouldn't fit inside the motorhome either. The car plus the motorhome plus a trailer big enough to load both would probably be more weight (and more tongue weight) than most class C motorhomes could pull.
The carrying capacity of class C motorhomes vary quite a bit, but it would not be unreasonable to find a 5000 pound towing capacity and 1500+ pounds of cargo carrying capacity without overloading anything. (The tongue weight of whatever is being towed would eat into the 1500+ pounds, of course). Anything much more specific requires checking on the exact model, its chassis, weight, and axle weights.
Flat towing the car requires a tow bar and a base plate on the car and, for safety, generally should have a braking system installed in the car. The cost for all that adds up. A tow dolly is probably the least expensive way to tow the car, though it's not as convenient as flat towing.
Make sure you budget some money for repairs and maintenance of the motorhome. A set of tires for a class C (on e.g. a Ford E series chassis) runs around $1000, for instance Most motorhome tires need replacing due to aging before they run out of tread.
If you're planning on living in the RV in a city, parking on the streets etc., as opposed to for instance having a site monthly in a campground, be aware that a great many cities do not look kindly on that and may have zoning and parking regulations to restrict or prevent such behavior.
