Your mom can't sponsor her for PR, unless she filled in an app for common-law sponsorship in your name, and forged your signature a bunch of times.
Are you saying your ex already came to Canada as a PR, or you think your mom sent in a fake application and it's being processed??
Regardless, inform IRCC immediately of the potential fraud. Note that your mom could get into serious trouble for this since forging names/documents is a serious offence.
Your mom could simply invite her in helping to get a visitor visa approved, and for that there is nothing you can do. But there is no forged or fake documents needed for this.
You can't sponsor your own kids for PR unless your ex gives permission, or unless you have full legal custody awarded by the courts.
I think thats the problem. My ex gf doesnt want to give her permission for my kids to come here that why my mom forced to sponsored her as well. Is there still a way to prevent her in coming here?