Nice finds dude. I've found 5 or 6 NY buttons and all of them came apart except for one tiny cuff. Some came apart in the hole, and others while cleaning. The 3 piece construction is much more fragile than a two piece button. However, one I found last year came apart and I was able to read the backmark from the inside, otherwise I wouldn't have known it said "Goldsboro Rifles". Which was a Confederate unit made up of a few North Carolina regiments. They served mainly with the army of Northern Virginia, and surrendered with Lee at Appomattox. This backmark is a scarce, rare, and valuable misapplied Confederate back to a Union front. They have been found misapplied to NY and Mass. Militia buttons. My button is in 3 pieces, and a dealer here in VA offered me $100 on the spot for it. No way I'm selling it!
Keep on getting those goodies, you've got the "golden horseshoe" my friend!
-Mike