I would first make sure that the retraining order is lifted before you make contact. Once you find that out then you can write her first. Focus your letter or creating a relationship with her. Do not focus on the past or even mention her mother. If you do mention her mother, it could turn her against you. Her mother is the parent that she knows, and speaking against her mother it will never be in your best interest.
When you write, even if she does not write you back keep writing. Staying positive, telling her that you miss her and how much you would like to start a relationship. Do not start off by sending gifts. She may think that you are trying to buy her love. Just start off making the conversation about her and trying to get to know her. Always remain positive and never harper on the the past. Even if she ask, give a vague answer. Do not down her mom.