How do I connect a 240 to 110V transformers that measures 55V AC on both the "hot" and "return" wires?
The output appears to be ungrounded or center grounded.  It could be a transformer intended for outdoor tools in UK.  If there is also a safety ground 3 wire plug, it could be coupling some of the harmonic current from the switch mode active power supply (which should be flowing equally on hot and neutral) on the safety ground.  That would be unbalanced current and trip the GFCI.  The smaller transformer could be wired with normal grounding or it may have a plastic case.  Adding filtering to the mains input could fix the GFCI issue.