I had this problem of doubling in my AyA Model 37 some years back, so I sent it to Jack Rowe in Enid, OK. Jack, by the way, is the premier expert gunsmith/gunmaker in matters involving AyA having been their representative warranty gunsmith whilst in England as well as here in the USA.
Jack quickly found the problem with my gun and advised me that the gun could double if either (1) the barrel selector switch was not fully seated in the selected position, or (2) if gunk buildup was in the area in which the select switch is trying to go, thus preventing the fully seating of the switch.
I also found out this normally happens when the select switch is shifted to the left barrel on S/S or upper barrel on O/U for the first shot, supposedly because the switch is normally set for the right or lower barrel, allowing gunk to build up on the other side. Then when infrequently selecting the other barrel to fire first, the selector doesn't fully seat and the gun may double. One of my AyA Model 56's (with single selective trigger) would also periodically double, generally during the end of waterfowl season. At the end of the season, I would thouroughly clean the gun inside & out, and put it away until next season.
Jack cleaned out the gunk, and I now frequently remove the sidelocks to clean out the insides. Since then, I have had no doubling in it. I also clean the inside of my waterfowl Model 56 each time I bring it home, thus stopping it from doubling.
I suggest before sending your Model #2 to jack Rowe, remove the locks and thoroughly clean the works, especially in the seats of the selector switch. Then if it still doubles, send it only to Jack. Jim Haynes