The fact Kaido blocks all of Yamato's attacks instead of taking them (as he took a Kong Organ casually) tells you, that Yamato hits hard. Always arguing with the Scabbards won't do any good, since Kaido's scales are vulnerable to Ryuo cuts but those Ryuo cuts are still shallow. And we won't assume that a slice from Kinemon > pre Udon Luffy's boundman attacks.
There is no way around it, Yamato is a top tier, being able to coat her attacks in CoC, using high level barrier CoA, having Kaido's moves and a strong mythical Zoan.
Maybe she even grew during that fight (hence "finally clashing equally with her father").
Ulti (ancient Zoan that endured Maser Cannon) recovering from a non CoC club of Base Yamato is reasonable.
Kaido sending Tobi Roppo after her is as dumb as sending Jack after post WCI Luffy + Law.