Hi Ashley! First of all, I think that it is wonderful that you have decided to do your first run. Disney races are the perfect races for new runners. They are great for all levels, but there are so many first-time runners at each event, that you really feel at ease and surrounded by great company when you are running your first race.
I am so sorry about your mother's stroke. Unfortunately, due to safety regulations, using a cane is prohibited in all races. I am sorry it took me so long to respond, but I was researching it to make sure I gave you the right answer. There is a non-racing wheelchair division in the 5K's that take place at every race weekend. That could be an option if you think your mom couldn't walk the 3.1 mile 5K without the assistance of her cane.
I hope that this helps and you guys find something that you can do together. I am sure your mother would also enjoy being part of a
chEAR squad to cheer on her two daughters in their first half marathon as well. ChEAR squad packages are available for each runDisney half marathon and marathon. Good luck to you guys and please let me know if I can help you plan for your first runDisney event! You will love it!