You should consult with an attorney privately. Whether the school acted improperly will defend on a number of factors including whether it was a private or public school, whether the video (and subsuquent review of the video) violated any laws, what the behavior was and whether it violateded any school policy or laws
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It is within the authority and responsibility of the District administrators to discipline any student for inappropriate behavior either on school grounds or which affect school activiities, for example, posting of information on electronic forums which affect students or school personnel. Facebook is notorious for posted information leaking out to the public. Unless you can prove that the administration got the information illegally (unlikely), there is little you can do.
That said, if your child's behavior was the manifestation of a disability (she suffers from autism, ADHD, etc.), then the District cannot punish her for that behavior. Again, you would have to prove that her behavior was from her disability.
You say it is "unknown" how the school got the video. Huh? The school got it off of FB, of course. Students don't ever seem to figure out that what is posted on FB is posted on the bulletin board of the world without limitation.
Posting a video of inappropriate conduct in or around a school restroom is a lawful basis for formal school discipline. Of course you have the right to appeal the discipline through the existing administrative appeal process established by your district. (The school will give you a copy on demand. Follow all of the procedural requirements exactly, especially the time limits.) But I would caution you against appealing if your daughter is visible on the video -- leaving her without a denial-based defense.
The problem with going through the appeal hearing is that it always -- ALWAYS -- gives the school even more info against the student than it originally had. That's inevitable in the process of taking testimony from multiple witnesses. You need to have a real sound reason for buying into that risk, a reason such as a rational and legitimate basis for thinking that the appeal will be successful. There is no reason to expect success on the appeal if your daughter was there. Talk to an attorney before you walk deeper into this matter than you are now.
Admin appeals are rarely successful because they are not a level playing field, not even intended to be. The appeal is about whether the school district supports the principal's judgment in the discipline imposed. You can guess how that issue is usually resolved.
Three days is a very proportionate penalty for this kind of conduct as a first offense. You may want to counsel your daughter to take her lumps and learn a lesson.
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