You may not like my solution for your situation. I'm a peacemaker, it's the way I was born, and I don't deal well with confrontation. But I do know how to smooth over people problems. I'd like to make it clear here that I do not condone the behavior of your daughter. Placing your grand-daughter in the middle is unexcusable. My mother and my grandmother could hardly stand the sight of each other. When we were all together there always was an underlying tension. And each were vocal about the other to the four of us girls. We were stuck in the middle, sometimes blamed ourselves, and had to walk on egg shells when mentioning one to the other. Don't let this happen to your grand-daughter.
First, it probably wasn't the best move to write your letter to your daughter. If you had issues it would have been better to face her in person. A lot of things can be said with body language and the tone of your voice that simply doesn't come through in a letter. But that point is moot. You did it and now how to fix it.
If writing is your forte then another letter, this time one of praise and an appology, wouldn't be out of the question. Address the issues that are already in the open...don't bring up any new ones. Offer words of encouragement, love, respect and wisdom. But this is not the best solution.
The best way to handle this, IMHO, is to have a talk with her. One on one. No one else around. The cell phones turned off. Set ground rules to begin with...like, no shouting, no calling names, no blaming, really listening to the other person. Both of you should agree to the terms.
Once this has happened then you need to bring up the letter and expand on what was said. Make sure she knows that this is coming from your heart. Let her know if your feelings have been hurt. DON"T accuse, belittle or blame her. Accept the blame for your part in this misunderstanding. Have a list of possible solutions written down so that both of you can go over them and choose what will work for you both.
Not only is your relationship with your grand-daughter on the line here, but the one with your daughter too. Forgive her mistakes, love her unconditionally, praise her often, be a positive aspect of her life and respect her right to making her own decisions and mistakes. You completed your job of raising her years ago...let it go.
When my daughter, now 29, left home for the first time I gave her a present. I had cut the apron strings off my favorite apron and had them framed. She gave me a puzzled look. I then explained the phrase "tied to your mother's apron strings" (—Idiom:.tie to someone's apron strings, to make or be dependent on or dominated by someone: He has never married because he's tied to his mother's apron strings. Origin: 1535–45). My gift symbolized her freedom as she became an adult...I'd always be there for her...but I would untie those apron strings and let her journey into adulthood be untethered. Have you untied those apron strings?
Good luck and God bless.