What exactly is the best course of action for this rediculous situation? Has she done something criminal? What do I do now?

I count at least six violations of the law in your short narrative, including both sides. This brings two thoughts to mind. Tolstoy wrote that happy families are not very interesting because they are all alike. Yours sounds interesting indeed. Second, it is probably true that if you are going to hit your mother that you do so in a hospital.

First, call a lawyer licensed to practice law in SD that specializes in criminal defense, as you are charged with an offense and anything you say can be used against you. Discuss with the lawyer whether the recording you made is legal under SD law, and it's value as evidence against your mother. You should also discuss whether your mother has committed a criminal offense (extortion comes to mind) by trying to force you into giving her time with the kids as a ground to change her story.

Second, call a lawyer licensed to practice law in SD who specializes in family law to discuss the issues of whether you can bar your mother from having contact with your kids under these circumstances. This is something you could probably do by yourself as parents, but under these circumstances, I suggest that getting legal advice on how to legally enforce it may be important as the case against you proceeds. Good luck.

DISCLAIMER
This answer does not create an attorney-client relationship or constitute legal advice. Instead, given the nature of this website, it is provided solely for informational purposes, for you to use as a starting point when speaking directly with a lawyer in your State. Do not assume that the legal theories I mention that pertain to NJ will apply in your State. The laws of each State; and, the facts of each case are different, and it is therefore critical for you to consult with a lawyer admitted to practice law in your State before making any decisions on how to handle or dispose of your case.