Ariel has a mother in the 3rd movie (Ariel's beginning) ;P

I would've said Pocahontas, but she has the mother-figure that is Grandmother Willow.

sure

The rest seem to be happy just having a father

I think Triton seemed pretty lost half the time. A mother for Ariel would have calmed him down.
I don't count the third movie as having a mother, she died pretty quickly. Belle and Jasmin do just fine without a mother, they don't even mention it, and another commenter is right, Pocahontas had a mother figure.
Ariel really just needed someone to understand her.

she seems the most unstable and like she needed the advice of a mother. All other 3 girls are stronger and were fine without a mom.

I think it would be good for Ariel to have a mother since Ariel really needed someone to understand her and accept that she really wants to go to the surface. Not only would a mother for Ariel would calm Triton but also try to find a better way to help Ariel win Eric's heart without going to Ursula.