The rule is pretty simple: whatever passport you use to enter that country, you are considered the citizen of that passport while you are in the country.
Also keep in mind, even if your child has US passport, BUT if both you and your spouse are Chinese citizens, Chinese embassy will not recognize the child's US nationality. They will likely deny your childs' visa request and issue him/her a travel document instead. If your child enters using the travel document, he/she is neither recognized nor denied US nationality. They will be free to leave China in the future.
Also keep in mind, even if your child has US passport, BUT if both you and your spouse are Chinese citizens, Chinese embassy will not recognize the child's US nationality. They will likely deny your childs' visa request and issue him/her a travel document instead. If your child enters using the travel document, he/she is neither recognized nor denied US nationality. They will be free to leave China in the future.
