On all doubles (shotguns) I've work on (Never worked on a double rifle...) the separate triggers are separate firing mechanisms, As stated that allows one to select which barrel fires. On a single trigger double, there a cam which repositions during recoil to select the second barrel.
If pulling the rear trigger causes both hammers to release, seems like a simple mechanical fix, where the rear trigger is contacting the front trigger to lift it.
I realize it is very quick, but on a double shot, are both barrels firing simultaneously or is there a slight lag in the second barrel going off?
Again, I have never worked on a double rifle, but I've been inside MANY double shotguns, to the best of my knowledge the firing mechanisms are the same (or similar); I just can't believe a manufacturer hasn't corrected the problem, especially in this day of law suits.
