My ex filed a false police report claiming that I strangled her and threathened to kill her so that I would not kick her out of the house for cheating. I was put in jail and now I'm facing domestic battery charges.
In the many years we have been together, I have never harmed her or threatened her in any way, shape, or manner. Although no longer together, her and I are on speaking terms and have put this issue behind us.
Unfortunately, the legal issues remain. The only evidence I have to prove my innocence is an apology card stating among other loving thoughts "i'm sorry for everything." Also, the police report states that there were no markings or other bodily harm on either of us.
Because I have a positive influence in my life now with God by my side, I have forgiven her and hold no ill feelings towards her.
She has lied to me (about the affair), and the DA, and now she is scared about the repercussions. She has not shown up for court twice, and each time the DA has gotten an extension. We showed up to court together the third time and prior to taking the witness stand, she fled the courthouse because she didn't want to testify against herself and get in trouble for lying. The DA was not very happy, got another extension, and now a warrant is out for her arrest.
The entire time my public defender has been advising me time and again to plea. I have told her in no uncertain terms that I did not do this and will NEVER plea and to defend me as aggressively as she can. She seems new and I don't have confidence in her but can't afford a private attorney.
What is a Material Witness Warrant? Can they pursue her at home or work, or do they just get picked up on traffic stops, etc.?
What is the penalty for lying to the police and the DA? How much trouble is she in?
Should I get my own attorney or just have faith in the system?

