-can you choose which order to fire in?

that's what double triggers are for!

that maybe what they are for but some double triggers will only fire in 1 order!

Which shotgun with double triggers only fires in one order?

Yep. Pick the trigger of one's choice and pull.

That is news to me, is it possible that you have confused single non-slective triggers with double? I have an AYA with a single non-slective trigger, fires right barrel first, then the left barrel on the second pull, no choice. But any two-trigger gun I have ever handled can fire the barrel that it is connected to independently of the other.

I am aware of one exception, a Czech made Brno O/U that had a complicated "hybrid" trigger mechanism, it could fire the bottom then the top barrel with two pulls of the front trigger or the top barrel only with a pull of the back trigger.

I believe he is referring to the Browning double triggers on their early o/u. You select the order of firing by choosing the front trigger, which then fires the bottom barrel, a second pull fires the top barrel. To change the order, fire the rear trigger first. A really nice way to select the barrel to shoot first

I didn't know that about early Brownings. thanks for the education!

So an out house or a rest stop, um.grin

If thears paper rest stop.

Triggers on shotguns are like rest areas, some are nicer than the rest.