Forgiveness is letting go of the negativity just so you too can be free, but I doubt we can actually forget the pain they caused us.

You say it so beautifully. Forgiveness is about letting go of that negativity, so that we too can be free from the burden within ourselves. But to be honest, it is almost impossible to completely forget the pain they caused. Maybe the pain fades with time, but somewhere or other its mark remains—which becomes part of our experience and strength.