The grounding rod or grounding to the water pipe would tell you if you have a camper ground issue. (if it works fine after you do that, the camper's ground is sketchy)
From what you described.. it sounds like the GFI are not wired correctly.
While a GFI can be daisy chained on the same line, making all the plugs 'baby GFI's (because the real GFI will pop if any of the plugs fault) I don't like the practice. If your gonna have a GFI its usually for a reason (near water) and why skimp of safety.. pay the extra and have them all GFI plugs.
I dont know off hand, but I am ASSUMING the GFI line is shorting and taking the other lines with it.. ie bad wiring, or a Mr Mouse has chewed wires and they are touching.
This is where that multimeter I told you to buy comes in. with breakers off, the continunity check should read no beep (no connection) between the legs of the plugs on different breakers. Ground should beep. If they are connected, you have bad/mis wiring or a short (mr mouse)