*blushes*
The reason why I am using a character related to a cannon character is because Trel's a purebloods. Granted, I do not know if the Trelawneys are in fact purebloods as Rowling did not mention it, so its my interpretive licence.
I agree about people who say they are the sister, brother, or cousin of Hermione, Harry or Ron. That makes no sense timeline wide, but some of us, have laid out a
Family Tree, that shows where the cannon people are.
How to deal with it? You make it part of the application process, give a small family tree (I'm a Nerd) and deny the ones who don't follow the rule.
Is it fair to make someone create a character from scratch? Yes...
Regulating it? Well, you could have the mods & prefects look out for that kind of RPing online and PM the culprits letting them know their error.