My former fulltime nanny was using my address for her children's immigration papers, dmv, and other bills without my permission. If I report her to immigration for address fraud, what are the ramifications against me by reporting this? What type of penalty will be imposed on her? Her children are already legally here. She was checking the mail before I got to it?

If she lived with you, what address was she supposed to use ?

Tick

Why don't you have a talk with her, instead of filing a report which might turn back to hurt yourself.

First I am not even sure it is a "fraud" except to you, if she did this without your permission, she was living in the US, and perhaps this is where she got all of her mail.

I doubt it makes any difference at all to immigration