How did my niece's face end up on my daughter's body after being backed up to Google photos?
This sounds like Google+'s Auto-Awesome smile feature. If you took multiple similar photos then Auto-Awesome will attempt to create a composite picture with the best smiles. Unfortunately in your case it appears to have thought that your niece and daughter were sufficiently similar that it put your daughters smile onto your niece.

You can see more information (and an example) on this site