I would say that if you do the train to Cannes, or just stay in Villefranche, your mother would be ok. Also, taking the train to Monte Carlo, and then taking a taxi ride home is wonderful!!! Even if you do not pay to go into the casino, just walk into the place, it is beautiful and this is an easy do for any age. You would have to probably take a taxi from the train station to the casino, but the town is beautiful and something you all would enjoy.
There are probably other things you can do other than kill yourself trying to see all the major sights in all the ports, for sure you can do that!! I just happened to have a majority of teenagers with me and thus we geared our tours around trying to do it all, and it was a lot!! And left us all tired, but satisfied. Trying to go with the wide variety you have would be challenging, but doable. I went through all the Disney excursions with my group and let them decide what they would want to try and see, and then we hired a private tour company to provide transportation and the guide. Anyway,that might be an option, so that you have more flexibility is hiring a private tour company. Also, I am thinking that if you do a tour, if someone got really tired, they could possibly stay on the bus and rest. I dont know that for sure, but just thinking, it makes sense. Good luck...