I believe the question of “to wear or not to wear” is a personal choice and also geographic location.
Canon 1171 states: (Sacramentals), which are designated for divine worship by dedication or blessing, are to be treated reverently and are not to be employed for profane or inappropriate use…
I doubt your mother has any bad intentions (like Madonna or Britney Spears) by wearing the rosary as a necklace.
However, be aware that wearing the rosary around the neck has become a symbol for some Latino street gangs (in America). Several school districts in the USA have banned the wearing of the rosary (on the outside of clothing) because of this.
While I haven’t read any accounts of innocent people being caught up in any gang violence because of wearing a rosary, I wouldn’t take a chance – especially if I were to be living in the Southwest United States.