Magnatom,
I would not worry to much the safety of the glass. It looks like it would be pretty hard to work out if the glass in laminated, toughened , or just annealled. You could Google around for the statistics of people seriously injured by sliding glass mirror doors. My guess is that the number is close to zero. However, as a parent, I appreciate your concern. Replacing the doors is going to cost a lot of money, if you go that route.
My suggestion is to keep what you have, and just stick on some safety film. Here is a link...
http://www.foliatecshop.co.uk/downloads/catalogue/family-protect-film.pdf
I have no idea about the resulting optical quality, but it will work. You can get this kind of safety film on the internet, and you can do it yourself. It will be a lot more economical than replacing all that stuff.
My two pennies, and good luck