If she doesn't attend classes, she should be able to participate.
Schools sponsor extracurricular activities for the benefit of their students. Not the community at large, and not kids from neighboring districts. Schools serve as community hubs (e.g., they're usually polling places), but that's a secondary function.
If you allow a home-schooler to march in the band, by what rationale do you deny a 17-year-old dropout a spot on the football team? If you open activities to kids who aren't enrolled in any classes, how can you bar students who are failing their classes?
If the activities are a right of taxpayers, how can you kick someone out of the band or off the team just because he's been expelled from school? Don't his parents still pay taxes?
Where I live, students with failing grades aren't allowed to participate in sports; my senior year (back when dinosaurs ruled the Earth), one school had to retroactively forfeit four games because an academically ineligible player was on the team. The same was true of any competitive event, from debate tournaments to band competitions.
My teachers had to forward my grades to the band director, and there was some heated negotiation one time when I had a three-day in-house suspension that would have overlapped with a band tournament. The band teacher managed to convince the principal to defer the suspension to the following week rather than bench the principal tuba (laugh if you must, but our band won trophies and the football team didn't).
If you allow homeschoolers into extracurricular activities, you're placing school administrators in the position of vouching for their academic standing -- something of which they have no knowledge and over which they have no control. It might be possible to devise some means of measuring the academic achievement and progress of homeschooled students, but that would involve the kind of intrusion that I don't expect many homeschooling parents to accept.
The solution, as I see it, isn't to push to allow more people into school activities, but to push for more community activities that aren't tied to schools. If there are enough homeschoolers, adults and kids from small schools, you have the core of a community band. Once it gains a little momentum, kids from local public and private schools will decide to play there instead of or in addition to their school bands.