DonaldsGrl103, I appreciate your respect for your mom's feelings. I'm assuming you're a 20 something so my suggestion would be to discuss the situation with your mom and find out what she would feel comfortable with, then budget accordingly. My DD25 works on the ship and although she's always been very independent, I expect to hear from her at least each time she's in Port Canaveral - especially since she has a free cell phone and is atrocious at writing.
Depending on how long your cruise is, maybe she would be comfortable hearing from you when you get on the ship, then from Nassau and then when you're back in port. If you're going to call from the ship, be sure she understands that it's just a QUICK, "Hi Mom, I'm fine" and NOT the time to hear everything about your trip.
If you're sailing on the Magic, cell calls from St. Thomas are often included in your national minute plans. Also you pass St. Thomas between 10pm and 1am Monday night on the way to St. Maarten. DD has called on her cell when they were sailing past St. Thomas then also.