At colleges like St Olaf, which is deliberately built for high level musicians who want to have a liberal arts education, the most common model is participating in ensembles (and many play several instruments at a pretty good level), taking music courses and lessons, perhaps a BA or a minor in music, alongside another major (often, math, but can be science or something else.) It’s not a double degree - gen eds are the same and thus overlap - but there’s still a high level of musical involvement and musicianship. It sounds a bit like what you’re after and can be cobbled together at many colleges that offer a BA in music.
In any case, based on what you say, it sounds like the path your parents would most approve of while preserving your interest in growing as a musician.
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