Cozumel used to be a sleeply little Mexican fishing village that had fabulous beaches and diving. Once the cruise industry found it, that all changed. Unfortunately, the infrastructure of Cozumel was not developed to handle 20,000 people walking around downtown shopping. It is crowded, the sidewalks narror and it is hot.
My advice would be to grad a taxi to one of the beach clubs and spend the day there. Your Mom could relax in the shade while everyone has a great time doing what they want.
Check out the special reports on the various beaches Cozumel offers on http://www.PortReviews.com
and that should help you make a decision.