My Danish wife overstayed a visa unknowingly by 3 days in 2009 (before we met) and has since been denied a business and leisure visa twice (once in September 2011 and again in January 2012) on the basis that she didn't show strong enough family and financial ties to the UK, even though she has been living there for 7 years and has had permanent employment with the same company for 2 years. She was never been denied entry to the US, but allowed to visit the country on parole in March 2011, which is when they told her she would have to apply for a visa to enter again.
We married in May this year and I have since received a visa/family permit to settle with her in the UK where she is based and has a permanent job. We are very keen to travel back to the US to visit my family, potentially for lengthy periods of time, but not looking to immigrate. What are our options?