Well I would say there are several factors at play here:
Biological bond. Yamato is Kaido's only child. Judge had 4 other children to spare. Killing an enemy samurai like the actual Oden is one thing, killing your own progeny that went out of your way to raise for two decades is very much different. Yamato, who told Luffy she was Kaido's son, fully accepting what that meant, must have understood that came with some value to Kaido.
Kaido has spared Yamato's life many times before.
Yamato challenged him, Kaido did not randomly beat her. And yet every time Kaido left her alive when a crueler monster would have disposed of such an unruly and insubordinate child long ago. This is Whitebeard beating Ace after every assassination attempt but still keeping him around the ship as one of his sons. It only encouraged Ace to keep coming after his life time after time, easy to do when you know your life is not truly at risk. Ace only came to his realization that Whitebeard really loved him after speaking to Whitebeard's other sons, Yamato likely has no allies on her side.
Kaido clearly values Yamato to some extent. He promoted this very rebellious child as the Shogun of his new empire, Kaido is not foolish enough to pointlessly kill Orochi and replace him with an easily disposable Orochi 2.0. Yamato is not a sacrificial pawn in an exchange here, she is gaining a lot of authority. Kaido sees some inherent potential in Yamato that can't be substituted by King, Queen or Jack, whether it's strength, leadership, possible future loyalty Kaido expects from a samurai wannabe. Has Kaido shown this kind of favoritism to Yamato in the past? Most likely. This led Yamato to again believe her life is of some value.
I think it's pretty reasonable that for once Yamato, so eager to fight Kaido again like she has many times in the past, has only just now realized the stakes. Kaido will kill her if she crosses a certain line. He's a monster, not a parent. This isn't a beating and back to her room anymore and Yamato's life may actually be at risk. For a girl who has been sheltered and in a sense protected in Onigashima all her life, it can come as quite the shock.
Not at all surprised, though I understand why Yamato would react that way. She challenged him all the time, and while Kaido beat her down each time in response, there was no implication that he had killing intent. It was only after she saw the cuffs explode did she realize that Kaido will kill her if she steps out of line.
Her reaction on-panel was a bit childish, though. I couldn't take it seriously at first.
Kaido cares for his daugther. Given kaido's durability and yamato being his daughter, yamato herself should have inherited some of kaido's durability. So I doubt that the explosion would have killed yamato.
She would be wounded and faint obviously, so she wouldn't be able to escape from onigashima, which is kaido's goaö from the beginning.
So it does suit him, a "monster" whl forces his will upon everyone else but "still" cares and is kind to his daugther (not killing her).
Oh and all of those beatings were probably for training, just likr with garp/luffy or wb/ace. This is kaido's way of showing compassion to his daughter, he trains her/ makes her stronger WITHOUT showing his intentions, because he IS kaido. A "hard" man but even he has a soft spot ik his heart. His daughter.
So I imagine that yamato wanting to be oden really hurt him, cause oden and kaido are polar opposites when it comes to character and ideals. So he was indeed angry whenever his little girl said that she wants to be oden.
Yamato has a right to be surprised because the father-child bond and her love for her father was blinding her. People who wanted so bad for Kaido to be a good parent despite all the signs he wasn’t, don’t. Unless their love for Kaido was blinding them too.