Shore Cord Failure - Please Help

Actually, a clamp meter can indeed be used around more than one wire, depending on what you are trying to measure.
Typically, around BOTH the hot and neutral wires at the same time.
This way, instead of the Amps pulled by whatever is connected to the line (which is what can make a thermal breaker trip), you can measure the leak current along that line (which is what can make an RCD breaker trip).

Same principle, it's just a matter of scale: when clamping hot+neutral together, the flowing current creates in each wire a magnetic field of opposite direction, but it's very rare to see zero as a net result, because there is always a tiny amount of leaked current along every line.
So, in one line which at any given moment is supplying say 30A, you should see 30 amps in the clamp meter by clamping either the hot or the neutral separately, while you're going to see just some milliamps by clamping both.
And only the latter is relevant when there's an RCD device tripping.