Yes, the first forms are the same: 1-130
After that, they're somewhat the same I-864 and DS-260
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The Daughter may be a U.S. Citizen through her Mother. For her Husband, she needs to file Form I-130 (the first step in petitioning for him). Once the petition is approved, the Husband can apply for an Immigrant Visa. Once the Immigrant Visa is issued, upon entering the U.S., he will be a permanent resident. You should consult with an experienced immigration Attorney.
She would need to file an I-130. You should seek legal advice on whether her daughter is a US citizen through her mom. This way her husband would be the only one need to become a lawful permanent resident.
The typical forms in an adjustment of status through a family based petition are the petition itself, an application for adjustment by the beneficiary, a medical exam report, an affidavit of support, a basic demographical form containing the applicant's basic info, and any additional form that may be necessary in the specific case. All of these forms require supporting documentation as well as accurate completion and signatures. All these forms are available for free at the USCIS website. Since this particular case DOES have some special issues, such as the citizenship of the child born in Mexico to a naturalized US citizen, the help of an immigration attorney is advised. I'd be happy to help. You may call me for a free consultation at 3239478490. Good luck!
If the child was born to a U.S. Citizen abroad, i.e. a naturalized U.S. Citizen who resided in Mexico at the time of birth of the child, then technically the child is considered a U.S. citizen if both parents were married at the time of birth and the U.S. citizen parent had been physically present in the U.S. or its territories for a period of at least five years at some time in his or her life prior to the birth, of which at least two years were after his or her 14th birthday. If so, then you need to register the child's birth certificate with the U.S. Embassy or Consulate abroad. There is no separate immigrant petition that must be filed but instead the U.S. citizen parent will file a form N600 for the child in order to obtain a certificate of citizenship. As for filing petition for the husband. The U.S. citizen wife (petitioner) needs to first file an immigrant visa petition on behalf of the husband (beneficiary) and pay the applicable filing fee. This would be form I-130 along with form G-325 for both the husband and wife. Once the I-130 petition is approved then the National Visa Center (NVC) will notify the petitioner to pay a visa processing fee and submit additional documents in order to advance the beneficiary's immigrant visa petition. Once the requested fee and documents are submitted to NVC, then the entire file will be transferred to the U.S. Embassy abroad. The U.S. Embassy will notify the beneficiary and request additional documents including forms DS230 parts I and II to be completed by the beneficiary, as well as an affidavit of support, forms I864 or I134 to be completed by the petitioner and to be submitted along with certain original supporting documents; i.e. birth and marriage certificates, police clearance, etc. . . The beneficiary will also be notified by the Embassy to undergo fingerprinting and medical examination. Once everything is completed and submitted to the Embassy, the beneficiary will be scheduled for an immigrant visa interview at the U.S. Embassy. Barring any unforeseen circumstances during the interview, and once the beneficiary's visa is granted, the beneficiary will be given time to make travel arrangements to come to the U.S. with an immigrant visa petition. After arriving in the U.S., the beneficiary's permanent residence card (green card) will be issued. Now, if the husband had been in the U.S. before and accrued unlawful presence during his stay for a period of more than 6 months or 1 year, then he will have problems with obtaining an immigrant visa because he would be technically barred from re-entering the U.S. for either 3 or 10 years unless he is granted an I-601 waiver. Good luck.