Could she give me paper knowing that I have a DUI and would that affect me if she tries to fix my papers?

Generally, a U.S. citizen may sponsor a spouse for immigration benefits in the marriage-based Immediate Relative visa category, so that the foreign national spouse may become a Lawful Permanent Resident (to get a "Green Card"). This is true regardless of whether the foreign national may have been convicted of a DUI offense. Of course, there are many other details that determine eligibility, including details about how the foreign national entered the U.S.; when he entered the U.S.; whether any other immigration application may have been filed before; etc. There really is no substitute for you and your wife to consult with an immigration attorney who, after learning all of the relevant information, could advise about eligibilities, options and strategies to attain your goals, and who then could offer legal representation in the often complex application process.