How is she getting your gmail -- through another webmail platform (like yahoo), or through an email client (like Outlook)?
I experience something similar when I was travelling with a friend a year -- I checked my gmail, logged out, and then she went to check her gmail ... and found it was still logged in for me. IIRC, I think clearing the cache completely did the trick. I'd advise your SIL to do that as a first step: go Tools > Internet Options > General > "delete" under Browsing History > select "temp internet files" and "cookies" then click Delete.
But without knowing where your email is showing up it's hard to say more.