Based on what happened so far, I would worry a bit. You need collision and comprehensive insurance, just like a car, to cover accidents that happen to the trailer. But the policy should explicitly identify it as a trailer and have different provisions than a car collision or comprehensive policy. For example, it needs to cover damage to electronics (tvs and computers) while auto policies often exclude those. It also needs to cover attached fixtures, e.g. awnings, antennas, etc. Sometimes these are considered personal property rather than part of the RV (my policy is that way). That's OK, but the default limits on PP are probably too low if it is. A typical policy allows $2000 for PP, but you couild easily have 3x that amount if it has to cover your actual PP (clothing, etc) as well as awnings, tvs, satellite dome, etc.
Also, ask about coverage for injuries to people on your campsite, e.g. somebody falls on your steps or gets burned by the BBQ grill. If you have homeowner insurance, that may cover it, but otherwise you may want to add "campground liability" for that sort of thing.
2004 American Tradition; 2014 Buick LaCRosse
Homebase in the Ocala Nat'l Forest near Ocala, FL