Here is an interesting essay for you, so you can think about different ways to study music, including a double degree in music and something else. http://www.peabody.jhu.edu/conservatory/admissions/tips/doubledegree.html
I am not clear on why you are thinking about music ed versus performance. Are you being “practical” or do you genuinely want to teach music in a public school?
It is fine to get a bachelor’s in music. A BM would be 2/3-3/4 music classes and that degree is as good as any other in terms of grad school, med, law, nursing school, or jobs in or out of the music field.
A BA in music is another option, and it often IS an academic degree (with varying performance components). Theory and aural skills, music history and analysis, ethnomusicology, music and technology, composition…Usually 1/4- 1/3 classes in music. Again, this offers many options for future careers or school, and doing internships can also help with that.
You can also do a bachelor’s in some other subject, and do private lessons and extracurricular performance.
Then there are double majors, and double degrees. Your parents might like the double degree idea 
But it is usually an extra year.
It sounds to me like you might want to do a mix of schools/degree programs, 2-3 BM programs and then some BA programs as well. The double degree option is offered at certain schools that people on here can tell you about.
But first, tell us why music ed is in the mix for you, because that might mean that a state school in your state would be well worth looking at. (And don’t forget there are grad programs for music ed if you do do performance BM or a BA).