My sympathies Mrsdof, both for what you are going through and your current hurt. I too would have been devastated. My way forward would be to assume that DiL was rushed and stressed herself, especially if she is a working mum, and inadvertently handled the situation badly. When you see her I would thank her for her sensitivity in not putting you on the form in case it upset you, but that you are perfectly ok with it so took the liberty of adding your name. Perhaps you could explain to your granddaughter when you pick her up from school that you added your name as well and ask her if she is ok with it. Then you can tell you DiL that it is what her daughter wanted as well.
I see my own daughter handle such situations less well than she knows how, simply because she is so stressed with juggling work, children, studying etc.
My best wishes to you, Mrsdof. 