Background: I'm a US citizen and carry a US passport. My wife is only a US Permanent Resident, and carries a foreign passport. She legally changed her last name with Social Security, but at this moment her passport and Permanent Residency card have her maiden name. We're planning a trip where my wife will need to apply for tourist visas to the UK and France/Schengen.
Questions: Suppose we do not have enough time to replace her passport and PR card to reflect her name-change before applying for her tourist visas...
Will there be a problem if she were to apply for the visas under her maiden name, and we make sure that her tickets have her maiden name?
Would the offices responsible for processing her applications notice her new last name through social security and then refuse her application because of the name discrepancy?
Can my wife re-enter the USA in these circumstances?