Would the US government deny my petition for my mother’s if she had a previous with her ex-husband?

When an adult U.S. citizen sponsors a parent to obtain immigration benefits through consular processing, that parent's immigration-related history must be revealed in the application process (and immigration authorities will have that information and the relevant files at hand even if a family wrongfully omits the revelation). Immigration authorities will review the old application file to assure an absence of inconsistencies and to assure that the old application had not been fraudulent. Additionally, it may be necessary to formally withdraw the long-pending application previously filed by your mother's former husband. It would be wise for you and your mother to consult with an immigration attorney who, after learning all of the relevant information, including details about your mother's immigration-related history, could advise about eligibilities, options and strategies and could offer legal representation in the often complex application process.