nankiee,
I have cruised 5 times. Two of those times have been during hurricane season, in August. There were no guarantees and I had to be prepared for a changed itinerary. However, I never experienced anything other than rough waters going back to Puerto Rico from Aruba. We just lost our balance a little while moving about the ship, nothing serious. Everyone seemed used to the motion of the ship by then. Fortunately we were able to complete the itinerary without a problem.
Sometimes the captain has to make decisions like missing or changing certain ports. Sometimes he may decide it's best to stay out at sea rather than attempt to challenge rough currents at certain ports.
You can rest assured that the captain is kept up to date about the weather and will put the the safety of the passengers and the crew first.
You may be inconvenienced, disappointed or you may miss out on something you really wanted to see, but the priority for the captain is safety.
As you can see by reading some of the postings on this board, storms occur outside of hurricane season too.
Having said all of that I hope you and your mom have a great cruise and calm waters whenever you decide to cruise.