Funny I found this thread today. Last night I was playing pickup hockey and noticed how bad my stickhandling skills are. For example if I push the puck to the left it's often out of my reach before I can catch it back on my stick blade. All in all I think it's because I'm right hand dominant shooting leftie, and I need to improve my dexterity, wrist and lower arm strength on my left side.
Stick handling either right-left or forward-back is like a game of catch -- one side "throws" and the other side catches. If there's a large discrepancy in muscle control between the throwing and catching muscles you're going to have trouble controlling the puck. I firmly believe that you can train your hands to work together if you know what exercises work and you practice regularly. That said, I have no idea how to approach this kind of training but I'm doing google searches for "dexterity exercises".
Anyway, I remember Sergei Samsonov said in an interview he learned some great tips from watching Alexi Yashin stickhandle around three pucks -- around the triangle, back and forth through the center, etc. IMO it's great to have "quick" hands but it's even more important to have longer, more deliberate moves where the puck seems glued to the stick blade no matter what direction it's going in.