OP, I am happy for you that you found the problem. Kudos to you that you did not blame the camp. You should not have had to try 2 other sites for power.
A multimeter is an inexpensive and valuable tool. So is a toaster or hair dryer to check voltage ( v/a) load (volt/ amperage) at the pedestal. Use a 30/20 adaptor, or even a 50/30/20 drop adaptor to plug in your hair dryer.
Did you ask camp maintenence to help? Check voltage, load test for amperage at the site? That could have saved you a lot of guesswork, and discovered your trouble easily.
Power faults do happen at the pedestal. Connections there get corroded, breakers get weak, buss bars overheat, may show voltage with a meter, yet not carry amperage.
Consider that rv pedestals are out in the weather. Just like your power cord. Moisture is an electrical connections worst enemy.
About equal times every year in my camp the issue has been ours, or the guests cable or connections like you found. Thats why in my previous response I suggested checking power at your first junction in the rv after you had tried several other sites.