I'm not sure if why we should even listen to what the Quartet have to say about the royal family. Everything about them is so confusing.
The Quartet goes back into hibernation to wait until Chibi-Moon comes of age/power. So they re-emerge in the future before she goes to the past again in the final arc, but it's clearly the first time Chibi has seen them in that capacity. So they go back with her and then spit out this toss-away line about one daughter so that Naoko can further insinuate that there's something odd about Chibi-Chibi (even though she's mere seconds away from revealing her real identity, whatever...)
But how would Vestas even know that? They only briefly lived in the present era as enemies, then for a few minutes as senshi before they went back to sleep. Then they re-emerge in the future and Vestas knows everything about the royal line? How? Did they maintain some level of awareness while waiting for Chibi? I'd expect this kind of knowledge from Pluto, but not the Quartet.
I don't think Moon explicitly passed her powers to her daughter. I think Chibi's power is her own, and Moon's just went dormant. But regardless, the one-daughter rule seems silly. QS only had one daughter and may have stopped there, but we'll never know because everything was wiped out before she even reached adulthood. As for Chibi... well, NQS doesn't exactly show a whole lot of attention and doting on her in the flashbacks, so maybe she wasn't too thrilled about producing more than one kid after having her.