When I was packing a SXS .500 NE double rifle over seas I learned that my shooting style had to change completely from the more familiar for me bolt action. The fingers on the forearm wrap around the barrels, and my trigger finger had to hook firmly around the trigger to prevent doubling. Surprisingly the recoil from doubling was not much different from firing a single shot, just the muzzle rose a little higher, as they happen as individual events rather at the same moment.
This rifle had two triggers however, and if yours has a single trigger and doubles I suggest that there is a problem with the mechanism. The recoil of your first shot should set the trigger for the second barrel, but it seems that it is releasing it rather than holding it in the cocked position until you are ready to fire. If this only occurs when you are at the range, I would suggest you load the rifle one barrel at a time and select you barrel accordingly, but if it was me I'd get the lock work checked out.