In rereading this for possible use as a reference for another question, I see I did not explain a couple of things clearly, and totally missed one - though the other answers indirectly addressed part of it:
1) the 110/120V versus 90V difference could well be, as other contributors said, a bad grounding issue - basically the difference between the voltage between lie and neutral (which is cut off when the GFCI trips) and live versus ground - you appear to have a 10-20V differential beetween the two, which wouldnormally be due to either a bad ground, or a ground rod (or grounded pipe) close to an electrical device putting juice into the ground like an air compressor or wellpump commonly. Basically, the neutral (which goes back to the utilityi ground) and your system ground (bare gorund) are seeing different grounds. 10-20V difference is not uncommon - during strong norhtern lights in northern states, or during electrical storms, cn reach hundreds of volts at times even without a direct lightning strike. I have seen voltage drop to about zero or go up to 400-600 or more on 120V circuits during strong northern lights, where they are affecting long transmission lines.
2) the 10V could actually be zero on that circuit, with bleed-over from interconnected wiring, from some low voltage device - some electronic devices and some chargers and plug strips and UPS devices sometimes bleed some different voltage in neutral than ground during use, as can MOV surge protectors. Commonly from 2.5-12V. Generally shows up in buildings where the neutral and ground are not interconnected at the panel, but very low amperage voltage diffferences like that can persist in a circuit even if its breaker is off.
3) the 10V could also be poor calibration of the meter or weak battery in the meter - check with the electrodes a couple of feet apart across a piece of non-electrified metal like a metal tabletop or metal trim or such - if it does not read zero that could be the issue.
4) I would check polarity, as other comment said - might be you have a polarity issue which is confusing the GFCI breaker. Or, it is as simple as one device is loading the circuit so heavily (maybe due to bad wiring that is not connected till something is plugged in) that adding a second one is just tripping the breaker because of excess current draw. This migiht mean disconnecting the wires at the panel, then doing a full continuity trace along the length of the circuit, tracing all wires and ensuring there is no cross-connection (without any loads on the circuit) between live, neutral, and grounds (though depending on your house wiring scheme, neutral and ground may be joined at individual boxes, rather than just at the panel). Also - remember seeing some GFCI/AFCI's which checked not only that the power passing through live wire matched that in the neutral, but also checked that the ground was not carrying juice - so if that is the case an interconnected neutral and ground can confuse it.
5) Defective GFCI - I have seen them (especially electronic ones) do some pretty unusual things - and some pretty impressive fireworks when they short out internally.