Which marriage date should I put on my I-130?

So I got married in Korea (to a Korean man) on Dec, 6 2013. Then, in order for Korea to give me a residence visa to live in Korea I was told that I MUST have a marriage certificate from both Korea and the USA. I tried telling them that America already recognized my Korean marriage, but they wouldn't budge. So we went to the States and got married again (in Las Vegas), submitted all of the paperwork, and I was issued a visa to live in Korea with my husband. However, now that we are applying for his I-130 I don't know which date to put. His "Birth Certificate" paperwork has our Korean marriage date on it. So should I just use the Korean date and not mention the American one? Should I let them know that I got married again or just not bring it up? Thank you for your help