I'll take a poke at this...
OK, pull your slide off. Right above the right grip panel below the slide engagement rail- you should see a half moon piece of metal sticking up. OK, pull off the right grip panel.
Now, there should be a long curved wire- the bottom end fits in a hole in the frame & the dogleg bend in the portion of the wire that curves to the left should be in a notch at the bottom of that piece of metal- NOT THE HOLE. This wire is a spring which holds/forces up the trigger connector (may not be actual name of part). Anyway, if that bar that connects the trigger and the sear/firing mechanism does not get pushed up- you should not have any double action going on. Look around this area and see if the wire/spring (or anything else) is not letting that piece of metal go upwards.
If all that is in good order and being pushed up, then I can only guess there is a chipping or breakage where it connects with the sear/hammer parts.
Also, check the rear slide rail area on the slide. There is a milled out area near that starts about 1/4" from the rear of the slide- it's rounded on the ends and reduces the thickness of the slide in that area by half. There should be no burrs or other obstructions in that area.
If the problem isn't there and easily fixed, then I'm sorry- I don't have any more ideas and can only suggest a trip to a Gunsmith. Good luck.
EDIT: Also look at the inside of the grip panel to make sure there is no burrs or debris that hinders the movement of that wire/spring and connector.