Upvote:1
According to Visa policy of the Dominican Republic, citizens of Mexico do not require a visa to enter the Dominican Republic (same as for US citizens).
Your student should have no paperwork problems on the trip and of course should bring both her Mexican passport and her US Permanent Resident card.
Note also that:
As of 1 January 2018 visitors to Dominican Republic are no longer obliged to purchase a tourist card as this fee is now incorporated into airfare.