I was 51 when I came out to my mom - she was 81 at the time - and she had a lot of trouble with my new name but she tried and she cared and that is what is really important. For 51 years I was her son Evan and life long habits do not break easy of quickly. Sometimes as a child she called me Ev for short and so we agreed that it was still appropriate to call me that instead of Eva. After about a year she started addressing letters to me in my full new name and has started using Eva more often with me on the phone. This has taken about 4 years for her to change and she certainly has the right to go at her own pace. You do too [mom] - so don't beat yourself up if you slip up once in awhile.
To your daughter I urge patience. I know that it is easy for me at 55 to say and it is hard to be patient in your youth, but remember little sister: time is on your side!
Sometimes we trans folks get impatient about our families catching up and using our new names. We want them to instantly understand and fully grasp all of our changes and be happy for us. But we must always remember that though we knew from early on we were different and have always lived with the inner image of our true selves, to others our change seems sudden and drastic and often very disconcerting. We have to give them the space to adjust too. We have to be accepting of them as they are, slow to comprehend as they may be and let them act according to their own perceptions if we expect them to accept us our way too. It is a long process for them to understand us. We must nurture them into understanding just as we need and want their love and acceptance."
Hugs and Blessings,