Have you read the interstate commerce clause? The plain words explicitly restricts federal power in this case (at least before our supreme court endorsed an evil pro-New New Deal case from the 1940s).
Also:
Article 4, Section 1: Full Faith and Credit shall be given in each State to the public Acts, Records, and judicial Proceedings of every other State. And the Congress may by general Laws prescribe the Manner in which such Acts, Records and Proceedings shall be proved, and the Effect thereof.
Article 4, Section 2, Clause 1: The Citizens of each State shall be entitled to all Privileges and Immunities of Citizens in the several States.