Also, I've only the Westerosi or Wilshire to look to for really in-depth articulations - though, there was a thread on r/bakker too - about the biology of it all. What does happen to a broodmare? What happens to generations of broodmares? Doesn't Esmenet's composition affect matters at all? Certainly, Kellhus is much less likely to have a girl resembling the Whale-Mothers with Esmenet?
Did I answer the questions at all?
If it was strictly a DNA thing, it gets harder to justify, but not impossible. As described above "double recessive" seems like a vague term but accurate.
Basically, in order for a specific physical trait (phenotype) to be exhibited, you have to have a corresponding genotype (genes/dna/etc.). However, it doesn't have to be, and rarely is, a 1:1 relationship. So, for the Whale-Mothers, you'd have to assume that there is a whole slew of recessive genes that need to line up for get the desired phenotypes. One of those genes would likely need to be on the X chromosomes so that you could make it gender specific. All male dunyain could be carriers after a time, but if you assume you need specific pairings of XX, then once they breed with a world born, you'd necessarily lose one of those X chromosomes, and thus negating the possibility of receiving all the necessary recessive genes for whalemotherism.
"Founder's Affect" is also likely happening. Even if only a tiny subset of the Earwa at-large human population has a certain recessive, or even a rare dominant trait, if but 1 of those original founding families had that trait it would likely exist far more frequently in the Dunyain population. Throw in breeding programs that are intentionally selecting for specifics traits, be it intelligence or whalemotherism, and even the rarest genes can be cultivated.
As for broodmares specifically, it would be extremely difficult, imo, to designate a specific family of females that did not become whale mothers. You'd have to always keep them separate from the genepool, basically running an entirely separate breeding program for them, which would get more and more difficult as the centuries went by. Probably not worth the effort unless there was some specific reason to have special subset of females running around.
This is why I invoked Wilshire's perspective.
Also, Wilshire, now that the book is out in the open we should check out your mind-map as the Survivor ruminates on the "twelve Germs," which are implied to be the twelve seed groups the Dunyain started with.
12 is, I believe, more than sufficient. I'd have to go back and check, but I think my original theory specified an absolute minimum of 8 genetically diverse individual families as genetic stock (ignoring alien genetics).