The thing is, basically no one will ever know her middle name. Do you use yours? (I'm assuming you don't have one of those names like "Mary Lou.") Her middle name will be reserved for formal paperwork and a very few social occasions or if she ever has to testify in court. So really, the choice of middle name doesn't matter in the slightest. Sure, a first name can have a powerful impact on a kid's life. But a middle name? It's the perfect time to go crazy (for the love of God, all you fans of "MyKinzee," take heed.)
So while I'm not a huge fan of the name Mildred in itself, I am a huge fan of honoring your grandmother by giving your daughter Mildred for a middle name. It makes a wonderful statement of love and respect. And I have no doubt that Mildred is going to seem lovely to you, your dh and the few other people who end up knowing your dd's middle name, when it's associated with the wonderful person she's going to be.