I agree with almost everything said here but perhaps before you hire an electrician to check it out, perhaps you should talk to the owners of the campground and check the outlet on the pedestal with a meter.
You didn't say, if you know, in what way your rig was effecting another pedestal. If you could post that here, we could give a better evaluation of what is happening.
You should at least test your power cord and transfer switch, maybe plug the power cord in the pedestal and see what happens. The odds seem to be in your favor but hiring someone to check out your RV and "their pedestal" without their permission is something you can do but expect to be responsible for the cost.