What time of year are you at Yellowstone? How cold do you expect it to be?
As a very, very rough rule of pinkie, one battery equals one night of furnace usage, at least in my mind. Obviously that depends a lot on the battery and the temperature; if the furnace is running more or less constantly it will use a lot more power than if it comes on for a few minutes every half hour or hour.
I would suggest getting the second battery, though it may well be possible to manage decently without it if you don't need too much power and the weather cooperates. You still may need to use the generator to recharge once or twice. If you don't have a multistage converter, that can be a quite slow process.
I also suggest getting something to monitor the battery state that's more accurate than the typical three light indicator panels most RVs come with. A panel mount voltmeter is a very big improvement; a trimetric or similar is even better but also a good bit more expensive.