GFCI Trips when Grounds Touch
Let's consider Joe. Joe is living on a boat, using a diesel fired heater and using the engine to keep the batteries charged. Someone suggests fitting a carbon monoxide detector.  Joe fits one in the galley, and the detector goes off. So Joe moves it to the bedroom, still goes off. Back to the store it goes, the replacement also goes off. Back it goes, Joe gets a more expensive one.  It also goes off.  Joe is going crazy - can't anyone make a reliable detector???
Laugh if you will, but this is how most people react to GFCI trips.
The evidence is leading you to a conclusion, so let's try it on for size: &quot;attaching the ground wire makes the circuit less safe&quot;.  Does that make any sense?  Of course not. The ground should always be connected, always.
What's happening is there's a second problem - which was always there all along.  And hooking up the ground wire improved the GFCI's ability to detect it.
Power is supposed to flow out the hot wire, through the appliance and back the neutral.  Any current moving on a third path is a ground fault.   The reason we started installing safety grounds in the 60s was to provide a reliable third path, instead of allowing Fate to choose its own, typically through a dying human.  So it makes perfect sense that installing/repairing a ground wire would increase a GFCI's sensitivity to ground faults.
Disconnecting the ground, thus, became a &quot;red herring&quot;.  It showed correlation, but not causality.
Now, you need to admit that you probably have a ground fault, and then just work standard failure-tree analysis until you find it. As far as the grounds, there might be diagnostic value in temporarily unhooking one, but don't see it as a path to a solution. You must finish with all grounds connected.
ThreePhaseEel was quizzing you about cable type because the usual reason for a ground fault on an outdoor run is use of NM-B cable, which is not rated for outdoor/wet usage, and the insulation will fail when wet.