[Jaymo]

Double triggers on a SxS shotgun only fire one barrel per trigger.
IIRC, front trigger fires right barrel and rear trigger fires left barrel.
There's no reason or need for them to have been designed to fire both barrels with one trigger, at once.
You risk cracking the stock by dumping both barrels at once.
Double triggers were for firing 2 shots in rapid succession, such as hunting upland game. Single triggers do the same job with one less trigger.
If one trigger fires both barrels at once, you need to have it repaired.

Double set triggers were used on some rifles to give you a light trigger pull.
Double set, single phase triggers require you to pull the the rear(usually) trigger first, to "set" the trigger/sear for a light pull, and don't allow you to fire without first setting it.
Double set, double phase triggers allow you to set the trigger for a light pull, or just pull the front trigger without setting it first, giving you a normal trigger pull.