Okay lets say character A has two spouses; B and C. And amongst these three, they have two children; Alpha and Beta. Alpha is the child of A and B, and Beta is the child of A and C. So what is the titles of these family roles. Are Alpha and Beta cousins or siblings? Is Alpha's relationship with C their daughter/son or their niece/nephew?
In the context of this family I would've guessed that the kids would be viewed as equally everyone's kid, even if only two of them were the biological parents. If the polyamoruous family is accepted in the society you're writing there might be the same thing - and maybe a possibility to adopt the kid so everyone would be counted as their actual parent in all ways but biologically. Unless C and B are siblings no one is the niece or nephew of anyone. ETA: If they are married to the two people separately then there is as much relationship between the spouse and the other persons kid as if they were divorced and then remarried - so more or less none. Then there might be the chance of them being called "uncle" or "auntie" in the way that some kids call their parents close friends that - but that wouldn't make them the kids real uncle/auntie.
I don't see how cousin/niece/nephew could come in--none of the parents are siblings of one another. If this were a divorce situation, where A marries B, has child Alpha, divorces B, marries C, and has child Beta, then Alpha and Beta would be half siblings, C would become Alpha's step-parent, and I don't think that B would have any specific named relationship with Beta. If all of these people live together, then I would assume that the kids would just be siblings and the adults would just be parents. If the relationships are simultaneous but everybody doesn't live in the same house, then I'd say the kids are, again, half siblings.
Okay let me provide more context...; B and C are NOT siblings nor are they related to each other but are married to the same husband, A. BUT they do live together in the same home, along with their two children. I'm going with a mythology-esque story, where some characters have multiple spouses, so this isn't like your current era family.
In that case, I'd assume that all the adults are parents and all the children are siblings of each other.