I have little experience with double rifles, but have shot two trigger double shotguns almost exclusively all my life. A couple of comments I might make.

I have always shot the rear trigger first on doubles, unless I needed a different choke on a shotgun. It was the way I was taught 50 years ago, and the reason was it was quicker to move from the rear to the front trigger. This is related to the second point...

I have seen this subject discussed here several times and even more often on AR, which generally mirror each other. Every time the discussion comes up, several pundits inject the "fact" that recoil is the cause of a lot of accidental doubles since it causes the hand/trigger finger to move back and hit the rear trigger. This is patently impossible. The gun is recoiling, not the hand. If you don't grip the stock, your hand will remain stationary while the gun recoils to the rear, moving your hand/finger forward in relation to the triggers. Recoil does not cause doubling from trigge contact. I believe it is generally caused by a reflexive action by some shooters in response to the first shot. I find it intesting that those shooters who report doubling generally report having had several doubles. The same thing is true among two trigger shotgunners. I believe the root of the problem is either an odd trigger technique or a reaction somewhat akin to a flinch.