At age 15 my daughter was mature enough to spend a year in Australia as a Rotary exchange student. (I took us 6 months to get her to speak proper English when she got home! LOL) So, not all girls that age will act like the stereotypical teenager.
I think a 6-month cruise through the Bahamas will be a great family bonding experience, perhaps the last one you may ever enjoy together. Georgetown would be a great place to spend the bulk of the winter season. With hundreds of boats congregated there each year, there are apt to be other boats with cruising teens for your daughter to meet and visit with.
If your daughter wishes to experience Mexican culture and learn to speak Spanish, include "Introductory Spanish" in her home-school curriculum. As she finishes one level, move her on to the next one. At the end of your cruise she should be fairly proficient. As was mentioned in another post, look into well-known home schooling curriculums. They are challenging and well respected by the educational community.
Rather than forcing your cruising agenda to meet your daughter's interests and learning needs, why not look into student exchange programs that focus on Spanish-speaking countries. You may find that she would be just as interested as experiencing life in Spain as she is in Mexico. For example, one boy who was an exchange student in my daughter's group, went to Bolivia and had a fantastic experience. BTW, exchange students to South and Central America, are usually placed in the homes of well-to-do, professional families. Your daughter may actually enjoy a higher standard of living with her host family (ies) than she does at home!
Anyway, just a few thoughts.
P.S. If your daughter is interested in journalism, encourage her to keep a daily journal and to take photos of interesting things she sees along the way. This may be something that will help her with college admissions in a few years.