Son who is alive, paraded around and about to be publicly executed in a broadcast to rest of the world.
Versus brother who had died years prior to his knowledge.
An important context here.
Whitebeard's crew is basically like a yakuza family. They will fight to save their member, but if the member is already dead, they would not fight to avoid more deaths.......the dude is already dead. Especially when the hostage situation is meant as a public challenge. If you don't answer that call, then nobody in your crew is safe.