To be eligible for the scrappage scheme, the owner must have been the registered keeper for a minimum of 12 months. This means that you were the owner of the car and when signing up for the scrappage scheme, the new car will belong to you irrespective of how the finance was raised. Of course if your mother sent you the money, you could show the money came from her through your bank statement if a bank transfer was made. For cash in hand, you wouldn't have any proof. Either way, the new car is registered in your name and owned by you and if you can prove the opposite, you wouldn't have been eligible for the scrappage scheme and could be asked to return the difference, that is, the £2000 vehicle discount price.
This is just my opinion anyway but you could contact the Citizen Advice Bureau for more help on the subject matter.