No civilian can have you deported, though she certainly can report you to immigration. They may or may not do an investigation based on what she alleges. Parents have the right to determine who sees their children. She cannot force you to allow her to see your children. Keep all evidence you can of her threats in case you even need to defend yourself.
She cannot have you deported. You may want to consider reporting her to the police if she continues with this behavior.
Samuel Ouya Maina, Esq. 415.391.6612 firstname.lastname@example.org Law Offices of S. Ouya Maina, PC 332 Pine Street, Suite 707 San Francisco, CA 94104
If you are a law abiding green card holder you have nothing to worry about. Your mother in law could try to report your conduct to the government but it should not affect you unless you are involved in illegal activities. It does not sound like this is an issue for you.
Parents have full legal custody of their children and grandparents have no "rights" to them under the law.
If she is harassing you then you should consider reporting her to the police.