A friend of mine had the same issue with her husband, who is a green card holder. She emailed the St. Martin Tourist Office in NYC. They assured her that all he needed was a valid passport, his green card, and an onward or return ticket. If you would like to email them, here is the email address:

newyork@stmartinisland.org

You can also go on their website. www.stmartinisland.org
Also, if her Ukranian passport is part of the EU, then no problem. To be safe, check with the tourism office.