I am actually surprised that a 10k gold piece would be affected by the relatively weak chlorine contents of a swimming pool. This makes me suspect that the piece was about as shoddy an item as you could find out there in jewelry-land. I doubt its gold content or its bulk composition. I could, possibly, see some weld/solder joints being weakened, but the entire charm dissolving enough to crumble seems extremely unlikely.
The gold itself will not dissolve in pool water. Secondary alloying metals such as nickel, zinc, or copper should not dissolve much in chlorinated pool water either. Acidic waters, perhaps.