Will getting cash aid affect his petition for me?

While receiving means-tested public assistance can interfere with adjustment of status eligibility, that generally applies to a foreign national applicant, not the foreign national's child, receiving the aid. It would be wise for you and your husband to consult with an immigration attorney who, after learning all of the relevant information, including about the application for and receipt of means-tested public assistance by your daughter, could advise about immigration eligibilities, options and strategies for you, and could offer legal representation in the often quite complex application process.