Theoretically possible, but loaded with potential problems. It would take a splitter that would pass power only from one leg to the tailgater, and specifically block the power (and satellite signal) to the other leg. Problem is that it would probably also block the cable signal. And, unless you make sure the satellite receiver (or whatever powers the tailgater) is turned off when you use the connection for cable tv you'd then be feeding power back into the park's cable TV system. They wouldn't like that.
For my money, too many possibilities to screw up. Safest bet is a completely separate cable run for the tailgater. Depending on where your satellite receiver is located, shouldn't be a major challenge. Before getting a roof-top satellite dish, I strung a cable thru the firewall under the dash, then up through the pillar column at the end of the windsheld to the sat receiver in the overhead. Just run your tailgater cable into the engine compartment when you use it. Make sure you dress the permanent cable so it doesn't lay on any of the hot things.
al