What proof does the biological mother need to issue when the child immigrates to the United States with her ex-husband's wife?

I can only give you Canadian immigration regulations for reference. In fact, many regulations in the United States and Canada are similar. Your ex-husband needs to download a form online, which is the consent form of the biological father or mother, that is, you need to sign the consent form allowing your son to immigrate with his ex-husband, and that consent form must be notarized.