The answer depends on both the length of the relationships involved as well as the age of the children. First, the child must be under 21 years of age to be eligible for sponsorship immediately with their parent. If the child is not included in the initial process (maybe they decided to stay in their home country rather than relocate with their parent), the U.S. sponsor can file the paperwork later to sponsor the child, but will need to provide information about the relationship between the child and the step-parent.
If the child is over 21 or it is not possible to prove any true relationship with the U.S. sponsor, the child will need to wait for their parent to become a legal permanent resident first and then for that parent to sponsor their child directly. The advantage of this process is that there are no issues qualifying for the green card since the relationship between parent and child is easy to prove, usually with a birth certificate.
