Just to add - depends what subject/ age range your wife teaches, but generally this time of year secondary supply teaching is pretty slow. Exam classes will be on study leave so most cover is dealt with in house. Also, the time of year to apply for September jobs is generally January - early June (so by now it may be somewhat slim pickings, depending on the area you are in).
The employer carries out the DBS check, but it would not hurt to have a US check to show she is not running from a life of crime in the US! I had to get a check from my local Sheriff's department for my first UK job in a school, despite the fact that I moved here when I was 20...