Sad situation but having a green card revoked is NOT easy. While there is a list of things green cards can be revoked for those reasons are seldom used. The only common most used reason is if a LPR commits a crime such as drugs, murder, etc...and once their prison time is up then they are almost always deported. Marriage fraud is quite difficult to prove after having children together. Immigration/USCIS will take the info but seldom act on it. Immigration's take on it is you should have done your "homework". Is that always right, no but it is their attitude. The sponsor has basically no rights once the deal is done. The only time I have ever heard of someone having luck getting a green card revoked is when the person had "conditional residence status" (when the marriage is less than 2 years the status of residency is called conditional and you must attend another interview after a period of time to prove that the marriage was in good faith) and when the appointment came to have the conditions removed it was determined that the marriage was a sham and the green card was revoked. But once someone has been granted permanent residence it is almost impossible for the sponsor to have it revoked.