If the safety of Japan is the only problem your mom has then it's not really a problem...
Just show her these:
Top 5 Safest Countries in the World - Associated Content
A Safer Society -- A special report.; Japanese Say No to Crime: Tough Methods, at a Price - New York Times
This one is probably your best bet:
NationMaster - Crime Statistics
This one compares different times of statistics relating to crime of most industrialized countries in the world.