Probably not. There are two reasons for this.
The first reason is a lack of surviving records (or lack of records in the first place). Millions of women in many countries worked as volunteer knitters, sewers, POW parcel-packers, branch executive members, canvassers, hospital visitors, letter-writers, record-keepers, VADs, drivers (etc.) for a host of national Red Cross societies (Canadian, British, French, American, German, Belgian, Italian, International, etc.) during both world wars. Your mother might have worked for any of these. Records of wartime local and provincial branch volunteers in Canada have long since been destroyed (if they existed in the first place), and the National Office never held comprehensive records of volunteers across Canada.
The second reason is a historic tendency to imprecisely use the terms “Red Cross work” and “Red Cross nurse.” Many women did what they loosely termed “Red Cross work” (raising money, knitting and sewing for soldiers, etc.) for a wide variety of wartime charities (including but not limited to the Red Cross) through their regular church groups, clubs, and workplaces. The Red Cross never had records of these volunteers, nor did all of this so-called “Red Cross work” actually have anything to do with the Red Cross itself. Similarly, many people used the term “Red Cross nurse” to apply to any woman who did some kind of hospital-based volunteer work, including hospital visiting, VAD work (untrained nursing helpers who were administered in Canada by the St. John Ambulance Association), or military nursing (trained nurses who were actual members of the Canadian armed forces).
The one exception (for which we do have records) comes from the Second World War. Canadian women enrolled in the Canadian Red Cross Corps who served in the Overseas Detachment or as Escort Officers on war bride transports are included in our service records of the CRCC-Overseas Detachment. These records are confidential, and can only be accessed by the women in question or their immediate descendants.