You may want to consider getting a wheelchair or scooter for the trip, even if she doesn't use one at home. Travel is much more tiring than regular activity.
The cruise lines often have shore excursions specifically labeled as being for those with limited mobility and/or in wheelchairs. For instance, here's a page from Royal Caribbean's website about their program: http://www.royalcaribbean.com/contentWithHero.do?pagename=accessibility_ashore
However, this may not be what you want. As an example, here's their Accessible Florence excursion, just so you can see what they mean by this (basically, staying on the bus, except of course to shop): http://www.royalcaribbean.com/shoreExcursions/product/detail/view.do?sourcePage=shorexByPort&ProductCode=LV85&DestinationCode=
I agree that if you can afford it, a private excursion will be better, as it can be tailored to your interests and your mother's stamina, and can be changed on the fly if needed. You may want to do this for at least one or two ports as a special treat, if you can't afford to do it for all of them.
Lots more information on Cruise Critic. For instance, here's their Disabled Cruise Travel Forum: http://boards.cruisecritic.com/forumdisplay.php?f=190. When you read the stories of people on kidney dialysis or tube feedings who managed to take cruises, you'll see that you can definitely make this work for you and your mother.