That is up to your daughter to break the law. Using other nationality is a ground for cancellation of Thai citizenship.
Its the Thai law -
THAI NATIONALITY ACT, B.E. 2508 (1965)
Section 17 -
A person, who hold Thai nationality by birth in the Kingdom of Thailand and has an alien father or mother, may be revoked of his or her Thai nationality, if it appears that:
(1) he or she resides in a foreign country, where his or her father or mother has or used to have nationality, for a consecutive period of more than five years;
(2) there is evidence indicating that he or she uses the nationality of his or her father or mother or other nationality, or has inclined towards the nationality of his or her father or mother, or other nationality;
(3) having committed any act prejudicial to the national security or conflicting with the interests of the State or amounting to an insult to the nation;
(4) having committed any act in contrary to the public order or good morals. The Minister shall order the revocation of Thai nationality in cases of (1) or (2) in the Court, upon request from Public Prosecutor.
Ok sorry, may not be illegal but certainly a ground for cancellation of Thai citizenship.