Is it’s safe to assume that the 12 den mothers are not as eager to have children in this current age as a Kiyoko?
Not speaking with authority on the race or the culture or the current population of Kitsuhon, but I don't think it's necessarily that they aren't eager. I imagine they love getting pregnant, being pregnant, and having children as anyone possibly could. The others aren't like Kiyoko though. She's been affected by the Astral Plane and gives birth so much faster. The others probably still have much longer gestation periods (like how Grainne has a much faster seeding birth than even Dorianne, who until that time was absurdly fast by dryad standards). So they probably spend a lot of time being pregnant rather than having kids, even if they are better at it (have less difficulties, pain, complications, etc.). Also, without there being a war for hundreds of years, they probably don't need to have been pumping out new kids and such. Remember, that the more kitsune, the more people need to be around to feed said kitsune with life-force. It's a lot like vampires, they can spawn a whole bunch or an army, but then they'd have to feed on more and more people, which means less prey for the others.
if so how do they and Keros view both kiyoko and Kinu who are now technically the 13th den mother and future den mother respectively?
I can't speak for how Keros views Kiyoko truly, but from all the scenes and words, he loves her and is thrilled and happy that she's free. It could all be a scheme or ruse, but he truly seems to love her (and most kitsune that he's ever talked about) as far as I can tell. I am sure he could slow down her pregnancies if he really wanted and he could probably tell/order her to do anything he wished and she would likely comply.
The mainland clans are probably more worried about the political ramifications of a second princess or house leader than Kiyoko having children, which is why there's a big scene about her formally renouncing her claim to leading the house (though she probably would be considered in charge of the Frost Wood outpost (Komari is the governor of it, however). As for how they feel about Kinu, they're probably going to wait and see what she does (depending on her personality, she may or may not even care about politics).
Just my thoughts on it, but I am just commenting on a fun topic.