After researching some and reading my Constitution, she is correct. The president may negotiate and sign treaties, but must be ratified with advise and CONSENT of the Senate by two thirds of those present. At which time the treaty becomes the "law of the land".
However, there are a number of Judicial decisions since that say treaties may not violate individual rights of the Constitution. It's a complicated issue, but in general treaties are lawful.
Once treaties are ratified, they become law. Can laws be unconstitutional?
No, of course not.