When parents ask me about what their children should be involved in as extracurricular activities, I remind them, whatever their children are interested in. If they have a passion, allow them to follow it.
She sounds pretty remarkable. Advanced classes with good grades. She has also shown she is dedicated to this interest.
Our daughter attended a fine Arts Academy for high school. She too was always in the advanced/honor classes as well as fulfilling the requirements to graduate with the extra Fine Arts Diploma. This set her apart, from other students applying to college. It showed she fulfilled the highest honors in 2 ways in High School.
She was able to keep up with all of her homework, projects as well as the extras that went along with her Fine Arts classes.. AND, she never took PE at school instead she also took Rowing classes for 6 years, so that she could take all 7 periods of classes. Yes, even through her senior year!
She learned to manage her time. She has NEVER had a set bedtime. Instead we made a deal with her a long time ago, that "you can stay up as late as you like, but you have to get up and be ready for school on time, or we WILL set a bedtime". She knew her limits. She is a smart kid. She was prepared for college and scheduling her own time.
I bet your child is too.
I get the feeling there is something else going on with your husband. Try to help him figure out what his concerns really are.
FYI, Your daughter has this passion, and the more your husband denies her the ability to participate, the more she will resent him. If she can keep up with her school work.. Let her try.