If they have a 50amp receptacle, it should work with the NEMA 14-50 plug for your Mobile Connector. That said, the Tesla Connector needs a working ground for it to charge. Sometimes these RV parks aren’t wired the best .... also — many times there’s a circuit breaker for the 50amp Connector. Make sure that baby’s turned on.
So as a Plan B ....
They might also have what’s called a “TT-30” connection. (travel trailer 30amp).
It’s 30amp, BUT only 120volts. It’ll give you about 7-8 miles per hour of range. Better than nothing! You would need a special adapter for it. There are two options:
#1 - easiest and safest, will automatically set the car’s charging amperage to 24amps. You just replace the plug on the Mobile Connector with it and go!
TT-30 Adapter for Tesla Model S/X/3 Gen 2 – EVSE Adapters
#2 - cheaper, but you MUST set the car’s charging amperage to 24amps manually. You’d use the NEMA 14-50 plug with your Mobile Connector, and put this adapter on the end. This is what I use:
AC WORKS EVSE Charging Adapter RV TT-30P 30 Amp Plug to 50 Amp Electric Vehicle Adapter for Tesla Model S-EVTT30MS - The Home Depot
Good luck!!