Wife: advantage or drawback when asking for visiting student position?
Be honest. Present it as a happy coincidence. That's what it is, after all. For example,


  I've always been interested in different research communities and paradigms, given how this knowledge can help me to work more effectively with others and to introspect my own methodology. My wife has been offered a place in [state] also, so this is a ideal opportunity in my academic career to gain the experience I've sought.