Philippine citizens who are lawful permanent residents of the US do not need a visa to enter Mexico for tourism, business, or transit purposes. They can enter Mexico using their foreign passport and Green Card.
Explanation:
Mexican visa requirements are based on nationality and residency status, not citizenship.
Philippine citizens are exempt from needing a Mexican visa if they hold a valid Green Card, a US permanent residence card.
This applies to all purposes of visit, including tourism, business, and transit.
However, if the green card is expired, but the traveler has official documentation proving their legal status in the US, they may still need a visa.
Since the name on the passport and the name on her Green Card will be different I would bring a Certified Copy of your Marriage Certificate as well
Once AoS is approved, we try to get a US passport ASAP
Concern is that I'm not sure if AoS approval is the sufficient for getting a US passport
She cannot get a US passport when her Adjustment of Status is approved - That only happens if she applies for and is approved for citizenship