Single triggers on double barrel guns are designed specifically to prevent this.
"Designing and building a single trigger for the double-barreled shotgun...is complicated by a little-known phenomenon called either the "intermediate" or "involuntary" pull. When a shoulder arm recoils, it carries the trigger hand backward with it. At some point, however, the recoiling arm meets resistance and rebounds. The rebounding action thereupon drives the trigger forward against the shooter's still-flexed finger, and the shooter involuntarily unseats the second lock.....This all happens so quickly that a gunner cannot avoid it by his own actions. Only mechanical means can negate firing because of involuntary pull by delaying the second trigger/sear engagement on a single-triggered double until the effects of rebound movement have quieted....
The single-trigger mechanism of a double-barreled shotgun,then, must be deigned and timed to negate the involuntary pull by providing an intermediate pause between sear engagements.
For if no mechanical consideration were involved, the shooter's involuntary action would trigger the second barrel immediately after the first while the piece was still misaligned by recoil energy. It would give almost the same sensation as a fully automatic weapon or a faulty firearm that "doubles."
Gunmakers circumvent the involuntary pull phenomenon by working delays into the single trigger, thus prolonging the time between trigger disengagement with the first sear and engagement of the second. There are two distinctly different methods of engineering a delay factor in single triggers. One is called the "three-pull" system; the other is simply known as a "delay-type" or "timing-type" mechanism.
As its name implies, the three-pull system requires three definite pulls to fire just two barrels. The first pull fires the initial tube, after which the trigger shifts to a second, or intermediate, stop position that prevents immediate engagement of the opposite sear. The involuntary trigger pull then releases the the trigger from this intermediate notch, whereupon it swings to the remaining sear. When dry-fired, a double with a three-pull single trigger requires three positive pulls to complete the sequence. With live ammunition, however, the involuntary pull is hidden by recoil disturbances, and the shooter must consciously will only the first and third pulls.
Very few gunmakers use the three-pull system, but Woodward, Holland & Holland, and Boss have experimented with it....
A single trigger with the delay-type or timing-type mechanism requires only two trigger pulls. But it also needs a mechanical pause to offset the involuntary pull, for if the single trigger is not in "neutral" for the short time after the initial voluntary trigger pull, recoil-caused involuntary action will discharge the double's second barrel prematurely....
Inventors have had great sport with the timing-type single trigger, fashioning myriad models..."
Don Zutz, "The Double Shotgun, Revised, Expanded Edition" pages 55-58, copyright 1978