Maybe the cockatiel died of fright and wasn't "killed" directly by Amber? Even if 100% mutt, dogs usually chase cats and birds, cats chase birds and rodents, etc. I had a cat who caught and killed a hummingbird once! It's very distressing when a pet kills another animal.

I'd maybe get a good-sized gift certificate to the local pet store for the neighbor? That way she can replace the bird or buy supplies for her other birds/pets and decide on her own timing to do it?

Hope Amber learns to "get along" with other animals. My neighbor's hunting dog, well trained, still was catching and killing rabbits in his yard before his owner could get him to stop. I only let my cats outside during weekdays when everyone's at work because we're surrounded by large dogs.