The oddest family RP server title I saw was something like "furry family rp".
Now a family RP would be fun if it had a competing families twist, like Capulets vs Montagues, or merchant families striving to become to most powerful in town. Then again, those would surely break down into TDMs.
Or maybe not even competition, just a family trying to stay alive through hard times, like the Great Depression, or WWII.