Driven keys are something that has always been annoying for me while rigging. Setting up one side is fine, however when you need to mirror those keys to the other side, you hit a wall. There is no correct way to do this built into Maya.
The best way is to use a script to automate copying the keyframes. The ones that exist however are either part of a much larger toolbox, or are quickly assembled code written for a specific project, and lacking a UI.
This is why I wrote my own script to not only mirror SDKs, but also copy the driving attributes to different controllers. This way, if you have a hand controller that controls all of the fingers simultaneously, you can copy the keys for each of those fingers to their own controller, without needing to create them separately.
Get it here on Gumroad for free (or pay what you want):Get copy_sdk.py
Place it in your documents/maya/scripts folder, then add a new shelf button with the following code to launch it:
import copy_sdk copy_sdk.open_ui()