Mother wan't custody to take American Citizen daughter back to Mexico

Father US citizen.
Mother Mexican citizen.(Illegally in USA)
3yr old. Daughter born and raised in US,
Couple married in US,
Mother wants divorce, Mother wants to go back to mexico and custody to take daugthter to live in Mexico with her.

Mother does not have a job in Mexico, daughter does not have medical insurance in Mexico,
Daugther will stay at grandparents house in Mexico where granfather is alcoholic and abusive.

Father has steady job (worked for same company for 8 yrs), own a home, medical insurance

Does my daughter has rights to stay in USA because she is a US citizen? are there any laws on this?
Can the judge let Mother take Daugther to Mexico where USA court has no jurisdiction?
Can a judge give custody to Mother even if Mother can not take care financialy of daughter

In my part there is no criminal record or abuse that will go against me, I'm just a father worried for my daughters well beeing.

Please help.

I'm not sure I understand. How were you married if she's in the country illegally?

Consult an attorney. Why not file for physical custody of the child?

To the question: Can a judge give custody to a mother incapable of financially supporting her child. This is the common occurrence in the family court system, which is why there is welfare and child support. That question is really moot.

Thanks you for your answer,
When my wife came to the states she came with a tourist visa and we married with that document, so when her visa expires she became illegal.

I did file for fisical custody and she is asking for the same so she can take our daugther to live in mexico, we have a court date for August 26,

I'm just worried and will like to know if someone have seen this scenario before, and who has better chance to keep custody of my daughter, and if there are any laws to give priority to an american citizen child to stay in USA rather that go to mexico.

If her visa expired and she took no measure to renew it, that could work in your favor. This may be a case where a judge may find that the woman cannot remove the child from this country for fear you may never see your child again. She's already demonstrated disregard for this country's illegal alien laws.

Good luck to you on your court date. I sincerely hope you retain physical custody of your child and that the mother is charged with remaining in this country illegally. That is against the law.