Why would my GFCI breaker trip when I flip a switch?
First, don't sweat bullets over the last guy's work. "The last guy did a bodge job and I had to fix it" are famous last words, said right before your project goes sideways into "hire an electrican" land. 

Stay in focus.  Keep the project scope as small as possible, don't try to fix two different things at once. 

"common" isn't

You mentioned "common", and that's a typical way an electronics or automotive guy talks about mains neutral.  In electronics, everything connects back to a "common" which is a big groundplane, or the chassis of the car, and in those cases, that is the normal current return.  Not in mains wiring.  

In mains wiring, the closest thing to "common" is actually the Equipment Safety Ground (green/bare wire), and it is not a current return at all (except during a fault condition).  Other than that, mains electrical is wired like an isolated system where both supply and return are 100% separated from the groundplane.  What's more, circuits are isolated from each other - or at least, they're supposed to be. The reason is EMFs and eddy current heating, but this also bears very heavy on GFCIs.  They work like this: 



The GFCI is a simple current transformer.  It wants to see currents are equal (sum to zero) in all conductors.

As said, circuits mustn't share neutrals, and you can see the havoc that would follow if circuits did.  Even if a circuit was not on GFCI, but it returned neutral on a circuit that was on GFCI, it would guarantee a GFCI trip on that unrelated circuit.

I think that is the root of your trouble.