Your info is wrong! Do not know who you talk to, but look online an ITN is a temporary work ID number! She can work and is a precursor for her green card! Make sure she files taxes and pays bills, and wait the 12 to 18 months for card! Apply for the card!
Get the Fiancee visa! 90-day U.S. visa, marry in the U.S. Apply for social security number and green card asap. She can work, and than travel freely back and forth to Thailand and to the U.S. Easier then marrying in Thailand!