I shoot double trigger and single trigger guns interchangeably, and have since 8 years old (I'm 55, now). Grew up on a double trigger. I cannot remember once getting mixed up when switching from double to single and back, although some shooters say they do. I think if you've never used double triggers, and want to learn to, you should shoot it exclusively for a little while. It will become second nature. Start out, as most folks do, by shooting the right barrel first (front trigger), then the left barrel. After this becomes natural, and it will, try shooting the left barrel first, then the right. One of the great advantages of double triggers is that, if your guns barrels are choked differently, you have immediate choice of chokes without fumbling with a barrel selector.
I would second the suggestion to lengthen the pull. In fact, I like to shoot as long a pull as I can mount comfortably. I was fitted as needing 15 1/4" (from the front trigger) but can shoot up to 15 3/4" well. Grasp the grip firmly, but not white-knuckle tight. Gloves are o.k., but they will not cure the problem. They will only keep the trigger from hurting as much when it hits you.
Work on why it is doing that in the first place. You will never shoot the gun well if, in the back of your mind, you are expecting it to hurt you every time you pull that front trigger. I prefer to pull the trigger with the pad of my finger almost down to the crease at the first knuckle. Never have a problem with bashing the trigger finger. I shot a straight gripped 32" Fox in the Ga. State Championships last year just for fun. Two hundred targets in two days plus side games and my only problem with tenderness was my right thumb which wraps over the top of the grip got very sore from the safety bumping it in recoil.
Stick with it, it's worth the effort! Stan