Are the trusts created here in the U.S. legal and binding in other countries?

No.  Trusts are only recognized in common law (English speaking) countries.  If she has real estate in other countries, her best approach may be to have separate arrangements in those countries, such as Wills which specify (as should her US Will) that the Will only governs property in that country.  She could have only a US Will with a special international certificate signed by an attorney but that could well be more expensive and harder to administer when she passes.