You can't sue the women's shelter for believing her. That's what they are supposed to do: believe women. As for your wife, you might have some sort of claim IF she admitted it, but otherwise it's your word against hers about what did and didn't happen.
Did your wife make these statements under oath? If so, she could be subject to perjury if she later admitted that she lied. However, if these were just statements made to a battered women's shelter, I doubt that you have any recourse. It is not uncommon for parties to abuse the legal system during divorce matters. False claims of abuse are utilized by less than ethical people in an attempt to gain an advantage in the divorce matter but there is little or nothing that can be done against them, even if the allegations are proven false. You may be able to use the false statements as a basis for an award of attorney's fees if the false statements unnecessarily expanded the litigation.
Almost certainly not. What you should have already done is hired your criminal and divorce lawyer to respond to the charges.
If you find this answer helpful, please mark it here on AVVO as helpful. In answering you, I am attempting to communicate general legal information and am not representing you (and am not your lawyer unless you sign a retainer agreement). Any information in this communication is for discussion purposes only, and is not offered as legal advice. There is no right to rely on the information contained in this communication and no attorney-client relationship is formed. Nothing in my answer should be considered as tax-advice. To ensure compliance with IRS Circular 230, any U.S. federal tax advice provided in this communication is not intended or written to be used, and it cannot be used by the recipient or any other taxpayer (i) for the purpose of avoiding tax penalties that may be imposed on the recipient or any other taxpayer, or (ii) in promoting, marketing or recommending to another party a partnership or other entity, investment plan, arrangement or other transaction addressed herein. Note that I am only licensed in Georgia and thus cannot practice in other states. I am also required to advise you, if your question concerns bankruptcy, that the U.S. Congress has designated Ashman Law Office as a debt relief agency that can help people file bankruptcy. State bar rules require that I disclose my name/contact information in any communication (Glen Ashman)
Sign up to receive a 10-part series of useful information and legal advice about the divorce process.