The tow dolly sounds like it is a mismatch in the wiring on the two. Most companies use a somewhat "standard" wiring pattern but it often gets changed if they are modded by users. The connection on the Rv may have the correct pinouts listed inside the cover flap but testing will be needed as it may have been changed.
However if it is correct on the Rv, they may say it is not a warranty item to fix the trailer.
2015 Winnebago Vista 31KE on 2014 chassis