Is it normal for my side view mirror to have a double image when looking at it?

Hello, No, this is degradation of the mirror itself. The lining from the back of the glass is peeling away, and it allows light into the glass from another angle, so you get multiple images in the glass. Replacing just the glass portion will be fine unless the mirror is only sold as an assembly. If you have other questions, or need more information, let me know, otherwise, here is a list of certified shops in your area with the training to repair your vehicle: http://repairpal.com/cadillac-within-10-miles-of-jacksonville-florida-32218