All sons and daughters of Mexican parents have the right to Mexican nationality regardless of their place of birth.
Do you have doubts about the errors and double registration of the Mexican Birth Certificate of your children? Solve your doubts about the double registration of birth certificate and dual nationality:
Corrections to the Birth Certificate
The names of one or both parents or of the son or daughter may be misspelled or only come with a surname of one or both parents, so it is important to make the correction in order to register the children as Mexican.
The information must not contain errors, otherwise the civil registry where the procedure is carried out, will not allow it to be registered if the surnames or names of the parents do not appear as in the official identification.
On the other hand, if you already have the Act and you have to change it, the process is different in each state.
If you are back in Mexico, the process to register your children may seem complicated, but it is no excuse for not doing it.
If you register them in Mexico pretending that they were born here, then your children will have two official identities, and it will be very difficult for them in the future, since they will most likely face legal problems.
If you want your children to have dual nationality, you must process a Mexican Nationality Registration Certificate and not a Mexican Birth Certificate: https://www.gob.mx/sre/acciones-y-programas/tramites-de-registro-civil
If by mistake you registered your child as born in Mexico, you must annul it by processing a nullity of Act through a judicial process, always with the help of a lawyer, which varies depending on the state where you live in Mexico.