If your brother concurs with you this it might be pretty easy.
If he moves out, she would have to follow. Simply go to the Clerk of court where grandma's house is and ask them (or consult with a lawyer familiar with such) to explain the details. If she was ever renting from granny (before "falling in love"), that might help get an eviction notice from court. Typically the bench asks to see "contract." How long has the girlfriend been living there ?
Some states have common-law provisions, so it's a sticky issue.
An alternative plan to eviction process might be time to consider raising pet skunks in the basement. Cheaper than a lawyer, and possibly even cuter than the girlfriend!