I've seen stories on the three RV website I visit regularly that convince me NOT to hook into the RV's system. There were tales from folks who tied in upstream of the RV's regulator about the long hose to the grill on the picnic table getting run over by people on bicycles and bursting. A very long flexible hose at tank pressure isn't a very good idea.
Other people tied in downstream of the RV regulator, but found that the regulator didn't have the fine control needed for the low flow-rate of a grill, compared to a gas stove or the furnace. One poster said he couldn't get the temperature of the grill down below 600 F, even with the temp control at its lowest setting.
For my Weber Q-100 grill, I bought a 10-lb "squatty" propane tank that has the same base ring as the 20-pounder. I bought a "base-ring stabilizer" from CW and bolted it to the floor of a stow-bin. It retained the tank so well that it didn't need secondary restraint. I usually only got it re-filled to about 5 pounds of propane so it was relatively easy to lift in and out of the stow-bin.
I was very comfortable with this arrangement. When we sold the RV, we kept the smaller tank to run the Q-100 as a back-up to our S&B's Q-220 when we need more grilling space.