Some are public and some are private depending on their set up.

Your current school is trying it on; LEGALLY, they CAN'T 'not let you go' ; they're running a school, not a gaol.

No-one in your current school or school district can stop you leaving their school in order to go to an online school. That decision is solely between you, your parents and the online school you wish to attend: as long as your parents agree and the online school offers you a place, it is no business whatsoever of your current school. Whether or not the online school is accredited is irrelevant; how, why, where and by whom you are educated is for your parents to decide, not the state, not the local school system nor your current school.

Neither you, nor your parents, should even be asking for your current school's permission: if your parents are agreeable to the idea of online school and you've been offered a place, your mum just needs to accept the online place on your behalf and then INFORM your current school that she is withdrawing you (INFORM, not ask!); she needs to present it to them as a fait accompli, something that is non-negotiable because, if they see any sign of dithering or uncertainty on her part, they are likely to lie through their teeth to try and keep hold of you (or rather to try and keep hold of the money they get for schooling you).

ADDED: According to the Virginia Homeschoolers website - they have a section r.e. online schools despite online students not being considered 'home schooled' in Virginia - your parents are not obliged to even tell your current school that you're leaving*, let alone need to have the current school's permission (!)

* Altho. obviously it is still good manners for your parents to let the school know you will no longer be attending.

(http://www.vahomeschoolers.org/law/virtual_academies.asp Virginia Homeschoolers' online schools page)

You contact your local homeschool office