I disagree - Scarlet's grandfather, Logan Tanner, was a royal physician. Winter's father Evret was a guard and Solstice was a seamstress. I doubt either had much contact with the doctors, and their parents probably didn't either. Cinder's father is unknown, but he was a) either a peasant or b) someone who willingly went into the caves with Channary because she died of regolith poisoning. I am more likely to believe the latter. I think the main connection between them is that they are all Lunar, not that they are related.
On the other hand, I always was a fan of the conspiracy theory that Channary grew jealous of Evret and Levana and decided to take Evret as a sexual partner with her bioelectricity powers, sneaking off into the regolith caves for a romantic rendezvous. This would make Winter and Cinder half-sisters, and would also mean that Levana would not only be Cinder's aunt but also her evil stepmother... sadly it's probably not true :(