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This type of outsourcing is fairly common. You would need to abide by Mexican labor laws not U.S. or Washington labor laws. Here is a good overview of things to consider: http://www.crossborderemployer.com/post/2011/03/17/What-Multi-National-Employers-Need-to-Know-About-Mexican-Labor-and-Employment-Law.aspx
I would suggest contacting a labor law attorney in Mexico to advise you of any specific rules and regulations you should be aware of.
Here is another good resource for certain forms that are recommended by USCIS http://hiring.monster.com/hr/hr-best-practices/monster-training/security-center/hiring-non-US-workers.aspx
You can do it through your U.S. company but having a company there that manages the regulations and compliance and management of the employee might be a good idea and you just have a contract with that Mexican based company. That might limit some of your compliance exposure here in the United States.
Let me know if you have any additional questions.