Thule and Yakima both state in their manuals that they are not designed for use on the back of trailers or other towed vehicles. They won't honor the warranty if used in this capacity.
I believe Swagman is the only brand that actually rates their bike rack for the back of a travel trailer, and then only specific models. Their disclaimer is very similar:
'1. Purchaser is advised that the load created by rack and bicycles will exceed the strength of trailer or 5th wheel bumper, mounting location or
the bike rack. The rack is not under warranty if mounted in this location.'