It sounds like your issue with your mother goes a little beyond just whether you should be allowed to play online games or not. Is the bigger issue that you feel the need for more freedom, that you feel hemmed in? If that is the case, communication could help.
Your mother makes rules for you because she cares about you and wants what is best for you. If you would like to discuss a change to the rules, here are some suggestions on how to going about doing that:
1. Be respectful. The more respect you show for her, the more respect she will show to you.
2. Listen. (Remember, you are having a discussion, not delivering a speech.)
3. Empathize. Try to see things from your mother’s point of view.
4. Offer solutions.
5. Courteously accept your mother’s decision (even if it is not the decision you had hoped for.)
Whether or not you can get your mother to change her mind on online games, learning to respectfully communicate with her on this issue will lay the groundwork to be able to discuss any other issues that come along. She cares about you and you care about her; you’ll be able to work things out!
jw.org > Bible Teachings > Teenagers > Young People Ask > How Can I Talk to My Parents About Their Rules?