Why didn't King Triton kill Ursula

Technically, although the contract is indeed indestructible for Triton's abilities to directly penetrate, any abilities Triton uses COULD force her back. And considering the only way to actually destroy the contract is to kill her, there was a way to destroy the contract. Namely, have Triton blast her when she tries to use the contract to shield her, then bend the beam so that it would force her right onto one of those spears hanging off the wedding ship. Sort of like how Goku managed to beat Cooler here: https://youtu.be/2vdrCwDChwI?t=184 or the Son family killing Broly here: https://youtu.be/wyt_KYjQGKI?t=185

But I can forgive this bit. After all, Triton needed to redeem himself of his jerk behavior towards Ariel, and Ariel still needed to undo the mess she in part caused.

In the Broadway show ARIEL gets (kills) Ursula

Smashes her shell

Because Triton is not a murderer

I really think its a simple as that, if she had threatened Ariels life or his life he probably would have fought her and killed her in self defense (like Eric did later when she was about to kill Ariel) but what she did at that point was legal...even though it was despicable.

She might have manipulated Ariel into signing the contract, but she still signed it...it would have been murder if Triton had killed Ursula just to get his daughter out of a contract she willingly signed. By law Ariel had bound herself to Ursula and Triton would have had to break the law to get her out of it...and how honorable a King would he be if he were to break the law to bail out his daughter?

Besides for the sake of the story Triton had to redeem himself for his previous actions and Ariel had to learn something too about facing the concequences of her own actions...it was a turning point for both those characters in the film.