The Personal Auto Policy automatically extends the vehicle liability from the pulling unit to a trailer for liability arising out of an auto accident. The additional cost to add a trailer to your auto policy is for the Comprehensive and Collision to cover damage to the trailer.
The Comprehensive Personal Liability on your homeowners policy includes premises liability and no fault guest medical coverage that also cover acts of the insured, family members & pets arising away from the premises.
If while backing your trailer you drive over another parties foot, that is an auto accident covered by your auto policy. When you unhook your auto liability stops.
While setting up if you lower your jacks breaking another parties foot, your homeowners would pay their medical expenses up to a limit of several thousand dollars without regard to fault. If they sustained serious injuries resulting from your negligence then your homeowners liability limit of up to several hundred thousand would apply. If while hiking you or a family member cause a rock slide breaking someone's foot on the trail below or if your dog ran through the campground and bit someone on the foot, your homeowners coverage would apply.
As MT said...
It is important that if you do not have a homeowners policy, to insure your trailer under a full timers policy with coverage for Comprehensive Personal Liability. Instead of just adding it to your auto policy that will only cover liability from an auto accident.