How to get around polygamy laws in the United States?

Hello, I am a US Citizen who has lived here for over 23 years. My first wife and I have been married for 27 years. I recently visited Saudi Arabia (where I'm originally from) and the opportunity arose for me to take a second wife. My good friend has offered me his daughter. She is happy to marry me and I am happy to marry her (no coercion involved). I would like to marry her when she turns 16 which is in a couple of months. It is legal for me to marry her now in Saudi Arabia but I want to make sure I follow State law which states 16 is the legal age for marriage with parental consent. Everyone has given their agreement; myself, my wife, my new bride and her parents. The problem is, I would like my new wife to live with us in America. I don't want to keep her in Riyadh . Even though I visit there 1-2 times a month for business purposes, I would like her to live with me as my wife. So how can I get around the anti-polygamy laws? My friend suggests to divorce my first wife (as she is a US citizen anyway), then marry my second wife and bring her here? Of course this is all just for legal purposes. I will be really married to both of them. Will this work? Any advice from knowledgeable persons will be helpful, Thanks a lot.