"My assumption is that the power cord for the trailer is 10-gauge. 50-foot RV extension cables are also 10-gauge. This jives with the chart I looked up... BUT"
STOP assuming. Instead, LOOK at the cable. The wire gauge is printed on the cable insulation. (at least it was when it was new) There's your answer. If the printing/embossing is no longer visible, pull the cover off the j-box where the cable connects just inside the RV. Look at the wire.
"Am I just over-thinking this?"
No. IMO, You aren't thinking at all. You are reacting.
Chum lee