My wife and I have been married for three years, and have one child. She is a U.S. citizen and I'm from Australia. She started the immigration process for me, and I now have conditional residency, but she says it runs out soon. She's threatening to not help with the next application, for permanent residency, but to divorce me and get me deported instead. Can she do this?
Your wife doesn't exactly seem to have your best interests at heart, so why are you letting her keep track of your immigration deadlines? If you find out exactly when your conditional residency runs out, and file the paperwork without her help, you can save yourself from deportation.
The application that you will need to file is in Form I-751, available from the agency now known as U.S. Citizenship and Immigration Services (USCIS, formerly INS). Download the form from the agency's website at www.uscis.gov. One of the first things the application asks is how you're eligible for permanent residence -- and one of the choices (box d) says "I entered into the marriage in good faith, but the marriage was terminated through divorce/annulment." So if you can prove that your marriage was the real thing, but that you got divorced, USCIS will overlook the fact that your wife won't sign on to your application.
Having had a child together will be the best thing possible for your application -- a copy of your child's birth certificate will be great evidence that your marriage was the real thing. You should also attach copies of other documents to show that you and your wife had a life together, such as joint rental agreements, utility, credit card, and other bills in both your names and sent to the same address, and joint bank account statements. Also include a copy of your divorce decree.
You'll need to file Form I-751 and the other documents up to 90 days before the date your conditional residency runs out. If you haven't actually gotten divorced, you may be eligible for permanent residency on some other ground, such as "extreme hardship," or if your wife has subjected you to extreme cruelty. For any of these, however, get help from an experienced immigration lawyer.