New to all this, checklist

The other thought I had was that the propane refrigerator by definition has an open flame that is vented behind the refrigerator. I have no idea what effect going down the road has on that flame. It would also make me very uncomfortable pulling into a gas station knowing that there is an open flame going in my TT.

GlueGuy,

I think your way of doing things is ok. I use the TV to run fridge, works fine. I get to site, I use shore power or propane. I am a huge cooler fan that has everything I need for week or more, not a fan of hanging out in grocery chains. Sure you have already checked your 12 volt charge wire to make sure it is adequate. It's each individuals travels, have fun.

On our previous vehicle (Ford Escape), the setup was inadequate to both run the refrigerator and charge the battery. Once I figured that out, I have only been running the refrigerator on propane unless I am on shore power. We have traveled extensively using propane this way and have not had any problems. The flame is in behind baffles and there does not seem to be a problem with wind going down the highway.
I have not tried our Frontier. I don't have an adequate meter to measure amperage being fed to the batteries while going down the road, so I have stuck with propane.