I don't think her being imprisoned is that unchangeable considering Kaido respected Oden and wanted a son and Yamato kinda fulfils both of those roles. Whole imprisoned plot is just Oda repeating himself where the "princess" is in need of saving - Rebecca - Vivi - Pudding and repeat
No it's a core component of Yamato's character.
It's a core component of Yamato's backstory.
It's the reason for Yamato's dream.
It is the entire reason Yamato is fighting Kaido.
It's not just a Princess thing, if you changed that, we wouldn't have Yamato but a different character entirely.
It's not that you can't change the imprisonment plot, it's that the end product wouldn't be "Yamato".
Changing Yamato's imprisonment would be like removing Ohara from Robin's backstory. Preskip Robin wouldn't be Robin anymore.
A Yamato that was never imprisoned is not the Yamato we know but someone else entirely.
So Yamato would know the location of Momo and would embark on her quest to track him down for Kaido but in reality she would wanna save Momo thus enabling Yamato still having her Oden plot while being introduced early
Kaido trusting Yamato with missions out of Onigashima changes their dynamic entirely. In your scenario Yamato has none of her personal motivation for opposing Kaido.
Like I don't think you understand how major the changes you're describing will be to Yamato. The end product will share nothing in common with current Yamato but liking Oden. And maybe not even that.
Yamato admired Oden in part because he lived a life free of all restrictions and external forces.
For Yamato to be Kozuki Oden is to be free.
If Kaido was not the oppressive father.
If Kaido had never tried to control her entire life.
If Yamato was never a caged bird, she wouldn't have latched on to the first beacon of freedom she found.
Even Yamato's aspirations to Oden are because Oden lived a life so much more liberated than hers.
and not making her a damsel in distress
Yamato never felt like a damsel in distress to me.
If your suggestions were implemented, we wouldn't have Yamato.
Kaido would have a daughter, but she would be nothing like Yamato.