I'm sorry for the loss of your DH.
As far as your SD, I don't think you did anything wrong. Your SD made it clear she didn't want anything to do with her father, so you were just following her wishes. If she regrets it now, that's on her.
As your head is all over the place, this might not be the best time for you to respond. However, if you don't want to leave it hanging and feel you'd rather say something, I would just be honest with her. "SD, I wanted to acknowledge your letter. As I'm sure you can understand, my head is all over the place right now and I don't feel able to respond properly right now. If I have something to respond with later, I will get in touch when things have settled a bit for me." Of course, if you don't feel the need to respond, that could be valid too. I'm not sure there is right or wrong here but it doesn't sound like this is the right time for you to deal with it. Make a decision later and put it aside.