I think you misunderstood gam a little. No, the Doctor cannot file anything with the court - s/he has no standing UNLESS it's a mandatory psych hold (and that takes a hearing and due process). Think "Baker Act" or similar. (This assumes that Mom has been in more than the 72 hour "hold" which doesn't require a court order).

One thing sticks out though. Dehydration and exhaustion are generally symptoms of something else - it's entirely possible (if not likely) that Mom is being treated for the underlying cause, and you won't be able to find out that cause (not legally, anyway) unless Mom herself tells you.