How long does it take to get the immigrant visa for the children of a US citizen mother? What documents do you need to file?

Significantly more information is needed in order to provide an immigration legal analysis for the children. Under some circumstances, they may be deemed to already be U.S. citizens, and then may benefit from applying for Certificates of Citizenship. There really is no substitute for consulting 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.