Do you own this box? And are you an electrician? It seems to me from your questions and comments that the answer is likely no to both. That appears to be single phase? Based on 1 wire coming out of breaker I'm now assuming this is a 30 amp 120V circuit and this is not a 240V circuit as I had previously assumed from your 30 amp comment. There is just not enough info to go on here for anyone, so my last and most significant piece of advice is to close it up and ask the owner of the box to send an electrician to troubleshoot this issue. You need a proper test equipment and experience in how to use it to troubleshoot RV park wiring, which can be different form residential, to determine what is causing your problem. Sorry I don't have RV park wiring experience so unless I'm on-site with a meter to figure out exactly what kind of power is coming into this box, what gauge the wires all are, and see more clearly how they've distributed it to the outlets, I can’t help further...
My honest suspicion is that you're asking this low amperage box to simply do too much. That is a small box even by RV park standards. Many modern trailers could not run off of that. There is simply not much there to run an entire trailer AND charge your car...I guess one more piece of advice: I'd seriously consider running your Clarity on gasoline if they can't upgrade that service box for you. But upgrading that box is probably going to require major investment of trenching heavier gauge wire from their distribution area all the way to your site...
I've refused to install car chargers for customers in residences with 100 amp service. So I can't recommend even attempting to charge a car from a residence that has 30 amp service...which is what I believe you have here.