Most applications actually ask if you have a relative that attended, although I believe it is only for relatives who attended the law school and not just the university in general. I would guess if an application asks "Have any of your relatives graduated from X Law School?" and you check no, then writing about how one of your relatives attended X University probably won't help.
Edit: Rinkrat y u poast faster than m3?
If it only asks about relatives that have attended specifically the law school I might just try to subtly work it into an essay, not base the essay solely on that fact. For instance "I first became interested in attending when I visited my cousin (who attended as an undergrad) and noticed how great the location of the campus is." Or something along those lines.