lc0338 wrote:
So even if the fridge is running off propane down the road I still have to have the batteries? Ok so since I am connected to shore power at my house now and everything is working then it's safe to assume to converter is working then right?
Yes, and yes. (There are, or at least were, some fridges which did not need 12V power, but they are very uncommon these days. You'd have to manually light the burner somehow, maybe with a pezio igniter button on the control panel. You almost certainly don't have one of them.)
You should have some sort of a battery connected up when pulling the trailer because the breakaway braking system won't work without a battery, assuming you have electric brakes. For traveling around where you camp at places with electric power available, a single 12V "Marine/RV" battery should be entirely sufficient and would be the most economical reasonable choice.
For more extended use without external power, a pair of 6V golf cart batteries (wired in series, to form a single 12V battery) usually gives the best bang for the buck if you have space for two batteries only. There are some more expensive and esoteric options that have more capacity...in many cases, a lot more expensive.