It sounds like what you are experiencing is purdy normal for the way most Travel Trailers are set up from the factory.
What I did was to convert my light bulbs all to LED bulbs. Then I put 2-6 volt golf cart batteries on the front where the single battery was. ( I had enough room to do that) . I try not to run the furnace much, only after I'm going to sleep and I keep the thermostat set at 62 degrees and cover up with a sleeping bag. By doing this I can camp a whole weekend on cool (not cold) nights with no problem.
I have a older camper so I also changed the converter (which has the battery charger built in) to a newer style.
We would need a better description as to what Travel Trailer you have to give a better judgment of how long you can go.
Be aware; if you ran your standard Travel Trailer battery all the way down then you have probably killed it. Most TT only come with a standard car battery and they are not designed to be drawn down to nothing.