As someone in higher ed for 30+ years (my first 6 coaching men's gymnastics (last 4 at the University of Georgia)), 6 more teaching coaching techniques and kinesiology - the last 14 as a faculty developer (director & lead instructional designer) I would offer the following advice if she wants to coach gymnastics (and/or any other athletic/health & fitness area). THIS is what I would do were I to do it over again!
Get a degree in Biomechanics/Kinesiology. This degree will require that your daughter learn; all the core (basic math, science, English, etc.) and then(!) human anatomy and physiology. Biomechanics/kinesiology... the science of movement - the physics and mechanics in any form of human movement. Apply every study/project to gymnastics skills/issues. Even basic skills when analyzed are VERY complex - and incredibly interesting. Sport psychology. Basic business management. Basic information processing - including multimedia and webpage/site design & management. Marketing and promotions. Dance. Nutrition. Athletic training, Human cognition (how people learn). Instructional design. Volunteer part-time in MULTIPLE roles at local gymnastics clubs - work with your college coach to gain experience in; recruiting (you'll be recruiting either gymnasts (as a university coach) or instructor/coaches at your private club before you know it. Meet management (it's complex when done right - a course in Logistics (business management) might be wise!).
She'll be so marketable - and uniquely skilled she can write her ticket.
MY 3 cents. ;-)
Best of luck! And by the way... the southeast (SEC) has some pretty good women's programs. My alma mater LSU is an up and comer... and they are going to have a new state of the art training complex in the new few months. UGA, Fla, Alabama, Arkansas... the weather here is just as nice (if not nicer) than California.
Steve