Did you completely miss the fact that like, WB’s whole speech to Shanks about avenging his crew was cap? He told Shanks he sent Ace to go after BB, but we literally see in the flashback that he actually told Ace not to go out of fear for his safety.
WB’s family protection thing is clearly a front he puts up to protect his own crew from other Yonko. The MF case was different since a son of his was about to be executed, in the case of Oden, he died years (possibly over a decade) ago.
Which means that Whitebeard was either planning going after Teach himself of backing Ace up with some other members, since the latter thought about how he ignored their warnings and just went off on his own on a whim. All of this assuming that Oda didn't just retconned that part of the story.
And why don't you think that, instead of a "front", Whitebeard told those things to Shanks in order to keep a strong facade as an emperor? Shanks was still his enemy, let's not forget that, why would he explain that Ace rebelled and left on his own?
Anyways, I insist, if I recall correctly we were told that Whitebard wouldn't ignore harm to his family even if the harmed was dead.
Ones dead the others alive. Preserving life >>>> Avenging it
First, it's not only about Oden but the Wano country and the people living there (Izou's biological family and friends, Ace's friends, etc.). Second, I don't have time to look for it right now, but I'm pretty sure that someone (maybe Sengoku?) stated that Whitebeard wouldn't stop if his son was dead.
????? THATCH WAS FAMILY.
Literally how is this any different with Kaido???
Whitebeard was going to avenge Thatch too, he just didn't want Ace to go on a rampage and alone because he was as aware as Shanks that he wasn't a match for Teach.