Ah social engineering this stuff is easy if you know how to play the game
I guess there is only a few ways you could really pull this off.
1. Beg and moan and whine till she gives in and just buys it to shut you up.
2. Help her around the house or do things the things that she really hates doing to make her life easier.
3. Compliment her on what a great mum she is and how much more you'd love her if she pays for your licence.
4. Send her on a guilt trip and explain that if she doesn't buy you this licence your life will be over, and you will turn to drugs and become a murderer all because she couldn't spare a few dollars to buy you a game.
If none of these work, combine them all into one and use the pokemon power card to double your skills.
** This post is purely a joke and i take no responsibility for your actions or the results of your actions. If you're put into a care home then its your fault **