A 15Amp circuit will easily run the converter (120Volt AC to 12Volt DC) and the fridge in electric mode. No propane needed.
Do NOT NOT NOT try to run the A/C, the water heater, or the microwave with this setup. You will either trip the household breaker or melt the extension cord (or both).
You don't say whether your trailer is at home or in a storage yard. If at home, you may want to have an electrician set up a 50 (or 30) Amp RV outlet. Make sure he really understands how an RV outlet is wired. 110 Volts; Split phase; 50 Amps. It looks like a 220 Volt plug but it IS NOT! Plugging into 220V will blow out every appliance in your trailer.
My Titanium is stored in the back yard with 50Amp power available 24/7. Be aware, however, that one reason I can do this is because I have a total of 500Amps (2@250 mains) on my main panel.
A fully charged battery, disconnected from any load, will hold charge about 6 months in Florida below Gainesville. About 2 or 3 months up North in Winter. People using remote storage usually disconnect their battery from all loads; or take the battery out and take it home and put it in trickle charge.
There are several good references on how trailer electrical systems work and the relationship of the 120Volt system to the 12Volt system. I believe one is "The Twelve Volt Way of Life" but it has been a long time and I don't remember where to find it.
Learning is part of the experience. We were all newbies at one time. (Of course, I'm so old that I learned on a two-ox cart.)
Formerly posting as "littleblackdog"
Martha, Allen, & Blackjack
2006 Chevy 3500 D/A LB SRW, RVND 7710
Previously: 2008 Titanium 30E35SA. Currently no trailer due to age & mobility problems. Very sad!
"Real Jeeps have round headlights"