What should you say in a letter to a family that is mourning the death of their mother?
Amber, firstly it depends on how well you knew the mother and how close you are to the family. It also depends on how you perceive life as a person & religion etc.

I might write something like this (assuming I knew the family a bit, but wasn't too close)

Dearest :

To apologise as people often do when someone passes away would be futile. I want very much to express my sympathy at the passing of your mother. I will remember her fondly, as she was a kind and generous woman....

Fondest memories and warm thoughts for the future,

This is how I'd write it, it's not completely typical, but I feel that in times like this nobody wants to receive the 'same old letter'. It's nice to receive something that shows you actually care, and it's nice to focus on the life of the deceased rather than the 'obvious' (recent death.)

If you are very close to the family, then I suggest you find out what is customary in their culture (for instance in Yugoslavia it is common to visit the relatives, whereas in England it is not)