Oda doesn't have to address the mom, Yamato being Big Mom's son would mess up the Charlotte Children list unless Yamato is older than Perospero. I really don't believe Kaido and Big Mom did it, and also there is still that slight chance that Yamato might not even be Kaido's biological son and that he might be an adopted son.
Disagree. It really doesn't matter what the children's list is lol, it can always shift down. The idea is that it would have been kept hidden anyway, considering there is a "surprising" announcement in relation to Yamato that MUST be announced after the alliance is announced. Kaido says it would have been confusing if mentioned earlier than this moment.
And yes, in this case, the mother IS important because while we know BM throws away her husbands and has 70+ children (so they aren't important), Kaido only has one son and is clearly his biological son from pure strength alone as we can see.
The question will be who in their right mind could bear Kaido a son? That IS important in the grand scheme of things.