Rights of the petitioning stepmother?

If she signs documents allowing him to take the children to the US, her rights would be very limited. She could at some point file a custody claim in a US court to try to get them back, but unless you and your husband are unfit parents, a judge would not rule in her favor. She could win joint custody, obtaining a legally enforceable agreement requiring the children to be returned to Mexico for a certain period each year. When the eldest child turns 21, he or she can petition the mother for immigration to the US if the child has naturalized as a US citizen. In the meantime, she is unlikely to get approved for a visitor's visa to enter the US.