I stand corrected, I think. On the trailers that I've seen that were plumbed for a gas grill, the grill being used was one of these
Sidekick Grills. They appear to not use their own regulator.
Now this next (clickable) picture shows the Sidekick Grill with a regulator on the bottle:
The question that I can't answer is: Does the OP's gas grill use a higher gas pressure than the output of the RV's regulator? A weak flame in the grill should be a sign of low gas pressure coming into the grill.
If the answer is no, then the 2nd regulator at the gas grill shouldn't be a problem as it makes the 2nd regulator redundant.
2005 Cruise America 28R (Four Winds 28R) on a 2004 Ford E450 SD 6.8L V10 4R100
2009 smart fortwo Passion with Roadmaster "Falcon 2" towbar & tail light kit -
pictures