I would definitely submit an appeal/ask for a remark, however is it possible that your daughter fluffed the exam? From how it sounds, there's a lot of pressure on your daughter - from her school and you, and it seems that she is incredibly bright and therefore probably puts a lot of pressure on herself. From the sound of lots of goods marks and one bad one, it does just seem like she had a bad day - if this was her first exam for the subject, or her first exam entirely, is it not possible that she's just had a bad day and that's that? From what I can gather about the Scottish Education system she will now go on to study the Advanced Highers (is this correct?) so can she not work on and improve this grade then, and learn from the experience that a bad day may just be a bad day?
As a good student (10 GCSEs A*-B, AAB at A-Level and now firsts in uni), I do understand how disappointing a bad grade can be, both as a student and also from the family point of view, but as a student I know that if I got a grade I wasn't pleased with, having a parent going online and threatening to call in the police or a handwriting expert would not be making me feel better at all. A bad grade isn't the end of the world, and what would be best for your daughter now would be going to make sure she's feeling okay, reassuring her of her ability and making sure she knows you're still proud of her grades and ask how she's feeling - maybe she wants to move past this and just focus on next year, rather than having to relive this bad grade?