She is not Margaret's twin sister. But, actually she is her half sister. Their age is only two days different. The mother and daughters doesn't know about this.
Chelsea is from the first wife(?), and her 'mother' is like concubine or something, and after the death of first wife, she become main wife. When the 'mother' gave birth, she is told that she have twins, but actually it is a lie from father(?). So, father actually lied to not only mother and daughters, but he lied to some government (forgot the name, it is like the one who files the population something.. consensus or another?? sorry english is not my native). There is a collaborator to make the lie as 'truth', as father position is not high.
Later, Chelsea get adopted to her real mother family.
Maybe, the abuse because the mother doesn't really feel that Chelsea is her daughter (even if she got told that she is) and with how different Chelsea with her and Margaret, she unconsciously alienated Chelsea.
And about the status thing is really tricky, and it is confused me. Basically, if people believe in one thing as fact, it will noted to status. that's why they really believe that Chelsea's relationship status is as Margaret's twin.
And how they know Chelsea is actually half-sister to Margaret?
It is because the black haired one (Glen) has a skill to see the true status (even the hidden one), but that skill is not the skill he can easily use. So when ppl around Chelsea really suspect her identity (especially with how rotten she get treated), he used the skill to see the truth