Can I have some help with my unforgiving step mom?

I have a step mom and when she married my dad she had a daughter. When they married I was 6 and so was her daughter. I was not nice at all to her daughter back then and my step mom hated me for it. I have changed now, and am a TON nicer, and me and her daughter haven't fought for years, but her mom still hates me, and she dosen't even live in our house anymore because she won't forgive me. I want to write her a letter expressing how sorry I am...what should the letter say??