Dear Having Fun,
Ahhh camping; driving on the open road, having the whole family together, cooking, cleaning up… Good God why would you do this? Anyway, in response to your question, while being towed, coverage is extended from your personal auto policy to your camper for liability coverage ONLY. The camper must have its own comprehensive and collision coverage that you can purchase on a separate camper or RV (Recreational Vehicle) policy. It is always best to purchase an RV policy as these types of policies can include basic liability, medical payments, physical damage, replacement cost, contents, personal effects coverage, trip interruption and towing. However, remember to never allow passengers in the RV/Camper while it is being towed or when it is parked and you are taking a nap.
As always, check with your Insurance agent or carrier to be sure your camper has adequate coverage.