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The so-called "right to work" legislation in Virginia can be found in the Code of Virginia, Title 40.1 - LABOR AND EMPLOYMENT Chapter 4 - Labor Unions, Strikes, etc, sections 58-69.
You can find more information about the Virginia law and the procedures related to it here.

But note that this relates to employers hiring non-union members. Your question asks about unions hiring non-union members, which may be an different situation, and may depend upon the specifics of your union's bylaws and relationship with the employers. Your union should have a legal counsel that is qualified to explain how the law applies.