Ariel's mother is Queen Athena, who only appears in the third film The Little Mermaid: Ariel's Beginning. She was killed by a boat when Ariel was five years old. King Triton never wants to discuss her is due to the pain he feels when her name is brought up. He truly loved her and that was very deep. In my opinion that is why he never remarried.
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Currently, Ariel is the only Disney princess known to have had a child. As for the reason why, my only guess is that this is because Ariel is the only princess to have had a true sequel movie. I say "true" sequel because Cinderella II and III consist mostly of filling in the gaps of the original movie's events-- very little is actually a continuation from the first story. And to my knowledge, none of the other princesses have had sequel movies at all.