Ultimately the only thing you can really control is whether or not the dog even has access to your dd again. I personally would not allow my child to return there under any circumstances until the dog was gone. Just hearing the dog bark in the crate might be enough to make her anxious, and that's totally not fair to your dd. Letting grandma come to YOUR house to watch her, totally fine, but not going there.
I did want to address her current fear of dogs, though, and tell you that she can eventually overcome it. It doesn't have to traumatize her for life. My ds was 3 when he was bitten by a family member's chihuahua. We knew the dogs were not friendly, and they were put away inside and in a locked room inside the house while we were there for an outdoor picnic. But a teen family member happened to be taking them for a walk when we were leaving the party. He had them on a retractable leash and pushed the button as he was walking toward us, thinking he'd be able to retract it and get closer to us to say goodbye. But the dogs surged forward and one got to my ds before we could blink and bit him right on his bare knee. Ouch.
Anyway, no, we didn't sue, we didn't report it, we cleaned up his knee and comforted ds and also the family member who was walking the dogs, and the family member who owned the dogs...everyone was crying...but it was truly an accident. Yes, the dogs are mean. But they took every precaution and sometimes things just happen. Now it's 3 years or so later. We have taken great care to be aware of and sympathetic to ds's anxiety over dogs. We've also taken care to expose him to truly friendly dogs, in small doses, and only as much as he was able to tolerate, until now he's at the point where he isn't instantly afraid. He understands not all dogs are bad. In fact, last Friday he went to a friend's house for a playdate (without me) knowing they had a brand new puppy, and he played with the pup and was fine with the pup being jumpy and mouthy like pups are.
I hope in time your dd is fine and no longer fearful.