"No, it was the first time I ever shot a shot Gun. I pulled the lead trigger and both barrels fired. Surprised the crap out of me. Then I learned I had to pull the rear trigger first then the lead trigger in order to fire them independently."

Navarro: There is a mechanical issue with this gun, as the front trigger should fire the right side barrel; as, with very rare exceptions, that trigger is always pulled first and set to fire the right barrel. If both barrels fire when the front trigger is pulled you likely have a worn sear that requires the attention of a qualified double gunsmith, as simul firing is potentially dangerous to the shooter and to the gun.

"What rounds I can use that will get the job done without such a kick. The job I'm referring to is knocking down targets.
- Proper distance for knocking down targets, I've been using 25yds. But then all I get is a big scatter pattern. Being military we like center mass. Do I go to maybe 15yds?"

You didn't say what type targets you were attempting to knock down; but if they are metal or anything heavy then shootig Win
low recoil/low noise ammo won't be the answer, as I don't believe those things are loaded in any shot size larger than size 7 1/2. For knocking down heavy targets you'd likely need to hand-load your ammo and use #4 shot or larger. And as to your "big scatter pattern", the barrels on your gun have been cut; there is no choke in those tubes, and a big scatter pattern is all you can expect from that gun. There are solutions for tightening patterns such as screw in chokes; but such custom work is expensive. As has been suggested, one can hand-load pressure suitable slug and buck shot loads; and reloading is an enjoyable aspect of using and shooting a vintage double gun; but if the shooting games you're into require heavy loads and lots of "knock down" ability, it's entirely possible that you have armed yourself with the wrong weapon?