When we look at why Whitebeard went to Marineford and not to Wano, the most obvious aspect is Ace was alive, Oden was long dead. So one is about preserving family, and the other would be about revenge for the sake of revenge.
But also Whitebeard probably viewed Ace the same way we the audience view Luffy— the future Pirate King and the Person who will bring the Dawn, etc.
So on a macro scale, Marineford was a lot about Whitebeard going to end his era (die), but in doing so preserving the next era and reignite the pirate era. And in this, Whitebeard succeeded, just not the way he thought.
The Whitebeard Pirates went to save Ace (the perceived next era), but instead the Whitebeard Pirates actually saved Luffy—the real future Pirate King. And of course Whitebeard sparked the era with his final words.
Throughout Marineford, we see pretty much every notable Whitebeard Pirate and Whitebeard himself save Luffy at one point or another. We also see Whitebeard’s last order is to protect Luffy. We see Ace, a Whitebeard Pirate, sacrifice himself for Luffy. On a micro scale, Whitebeard lost the war vs World Government but on a macro scale he accomplished the goal. Whitebeard went to Marineford to end his era, and preserve the next one, and he actually succeeded in this by saving Luffy and declaring the One Piece is real.
As for Oden, he entrusted Wano’s future to his Scabbards and children. In the years he was dancing, he never once tried to discreetly contact Whitebeard and charge him with helping. Oden bought into the 20 year prophecy that we are seeing come to fruition now.
*Theory by ahood34