Doubling can have many causes ranging from worn sears & notches, gummed up or worn mechanicals like the cocking hook or cocking slide to stock head wrist screws tightened to tight causing lack of clearance between the trigger blades & sear levers which doesn't let the gun cock completely. One quick check for this is to cock the gun unloaded and then wiggle the triggers front to back and make sure there's some slack in the triggers. If they are tight, that could be your problem.
Another one is having the correct trigger pull on the rear trigger, if it's to light the sear could dislodge on firing the right barrel. There's reason why the rear trigger purposely has a heavier trigger pull than the front trigger. These are old guns and who know what may have been done to them over the years.
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