Your problem was all about your inverter to battery wiring. The batteries had enough juice to run the inverter running the TV/DVD.
You can do the extension cord--except the cord has to go inside to where the tv is. Leave the door or a window open? Freeze to death, or have mosquitoes inside?_
Lucky you, there is already a cord you can use and it goes inside called the shore power cord.
๐ See my earlier post on that.
To avoid the thin wire cig plug (8 amp limit) with the small inverter, you can use short wires from the inverter clamped to the "battery lugs" at the 12v fuse panel. Those wires from the panel to the battery are fatter than the ones to the 12v socket at the tv panel, and will do much better.
Problem there is tripping over the inverter on the floor and the power bar in it that the TV and DVD are plugged into, when you or the kids get up during the movie to get something from the fridge. Plus when the inverter fan comes on you have to turn the Tv sound way up. So back to the shore power cable method. Lots of people do that.
1. 1991 Oakland 28DB Class C
on Ford E350-460-7.5 Gas EFI
Photo in Profile
2. 1991 Bighorn 9.5ft Truck Camper on 2003 Chev 2500HD 6.0 Gas
See Profile for Electronic set-ups for 1. and 2.