In The Little Mermaid, Ursula is actually Ariel's aunt.
This is revealed in deleted scenes found on the 2006 Platinum Edition of the film on DVD. Early concept ideas for the movie featured Ursula as King Triton's evil sister; however, there is no direct indication of this relationship in the animated film's final version.
Disney may have had a change of heart, though! We did a bit of digging and found that a song from The Little Mermaid Broadway musical DOES reveal Ursula to be Ariel's relative! Take a listen and see for yourself - Ariel calls the evil sea-witch 'Aunt Ursula' in the tune "Sweet Child!"