Depends on your draw, and the wattage at which your camper's converter can recharge the battery. I don't know enough about the converters to know how quickly they are capable of charging. Let's say your converter can charge the battery at 30 amps. 5A * 12V = 360W. This means that tiny guy will do just fine, for the most part.
But let's go beyond that. You have lights in your trailer, and heater. I know the heater in my trailer uses about 100W while running. Incandescent lights will use at least 10 times as much power as LED, so there's a lot to calculate here. The standard bulbs in my trailer used 25W before I swapped them to 1.5W LEDs. More than 16 times as much energy. I'll just go with the 25W value for simplicity.
-Assume you use 4 hours of heater @100W. That's 400Wh.
-Assume you'll use 4 lights for 3 hours. That's 100W * 3H = 300Wh.
===TOTAL: 700 Watt hours
If your converter charges at 360W (30A @ 12V), this means that you'll need 1.95 hour (2 hours) to charge the battery based on what you used (700 / 360=1.944). IMO, you'll be fine.
HOWEVER, when I was at Yellowstone, doing what you were doing, I wasn't at the campground during generator hours (8am-8pm) long enough to charge back what we used. 2 hours is a lot of time to sit there and wait for your battery to charge. This is why I went with a portable 100W solar panel, and swapped for LED lights. It would take 7 hours to recharge your battery with full output from a 100W solar panel. Grant Campground in Yellowstone was well-treed, so not sure how effective solar would be there.
And whatever you do, don't buy solar panels at HF. They are WAY overpriced. It's like $200 for a 45W panel, which is a massive ripoff. I bought my 100W panel for less than $200 on ebay. It is always enough to charge our battery throughout the day, as long as we have a good amount of sun. We also occasionally run the battery.
You might also be better off with a generator that has the ability to charge a battery, rather than running through your trailer's converter.
TV: 2013 Ram 2500 4x4 mega cab w/6.7l Cummins
Trailer: 2013 Palomino Puma 27SBU