@magicianjoe
No offense intended but I see a few things wrong with your theory.
First, Miss Bakkin is very old. I doubt Kaido would've knocked her up.
Second, why would Bakkin lie to Weevil about him being the son of a former Emperor (Whitebeard) when he is already the son of a current Emperor (Kaido)?
Third, why would Kaido allow Yamato to leave Wano (knowing that Yamato may go off and pretend to be Whitebeard's son)? I would assume that Kaido or King would've gotten rid of Bakkin if they found out what she was doing with Kaido's son.
Four, Kizaru was seen talking about Weevil as a Shichibukai (chapter 802, page 7:
https://mangadex.org/chapter/106174/7). I doubt the Navy's intelligence is so bad that they don't even know that Weevil is actually Kaido's son.
I'm not saying that your theory is impossible but it's very improbable.
Yamato is most likely the shadowly figure that we see in chapter 979, page# 10:
https://mangadex.org/chapter/900181/10