I am not an Oklahoma attorney, but there are some common sense steps you should take immediately. One is to talk to people who were at the school when Ms. Psycho pushed you. There are witnesses. You need to find them. Yes, you should also contact a criminal defense lawyer to protect you, and yes, he can investigate this for you.
But I want YOU to do it, NOW. Why? Because if you find witnesses who will sign statements saying that Ms. Psycho pushed you and that you pushed no one, this can be given to the police and prosecutor, so that they have this information when they review the case. If only the idiot's one-sided lies are told to the Prosecutor, then you can imagine what they will do. I am hoping that you can prevent any charges from being filed. It is much better to prevent charges from being filed than winning an acquittal.
You should also positively get a civil restraining order to keep this woman 100 yards or more from you and your husband. The witness statements you get from the school will provide the basis for getting this. You have to keep her away from you, your husband and the child, or she will fabricate other incidents like this. Next time she may escalate the accusations. By the way, staging an assault like this in front of her daughter is child abuse.
Get moving. I am glad for the child's sake that you won the custody dispute, but you have to protect yourself too. Once you are cleared of this incident, talk to the prosecutor about investigating/prosecuting her for the false complaint. Also provide to DHS copies of any court papers, including the resulting order, that chronicle the school incident, so they will understand what she is about for the next time she calls them.
I would also suggest compiling a package of papers (court petitions, declarations, witness statements, court orders) that help document and explain this woman's demented behavior over time. Make several sets of copies and keep them ready. Provide them to each investigator that she sends out to you. It will shortcut things to have them ready. She will eventually stop doing it when she realizes everyone is wise to her.
But I also want to caution you that based upon 34 years of dealing with dysfunctional people on both the civil and criminal side, my impression is that this woman is dangerous. Do not underestimate her. When her games do not win her control, she will escalate.
If this woman has visitation rights, you might also consider going back to court and letting the judge know about all this drama. This woman is a very bad influence on the child and the child should be protected from this insanity. Good luck. My sympathies and God Bless you for suffering so much to protect your husband's daughter.