Twins are huge in this novel, which is why we're analyzing Pet and her jealous maid, Tattycoram, together.
Actual twins, doubles, shadows – they're all there, lurking around corners being sinister and creepy. Which makes it all the more surprising that one of the characters who is a twin is cheery, silly, bimbo-y Pet. The fact that she had a twin sister who died in childhood certainly helps explain why the Meagles have raised their surviving daughter in a totally sheltered and babied way. But still, there is a lot of strange talk about the dead twin, with Meagles and Arthur jointly pretending that the dead girl was actually meant to be Arthur's bride. She kind of exists that way in both of their minds for a time.
And of course the dead twin gets replaced with a poor substitute – Tattycoram. The Meagles took her from an orphanage and raised her to be Pet's maid and companion. This sad young woman is not Pet's equal, but she is certainly her shadow and double, always in the background pointing out the cracks in this seemingly super-happy, super-normal family.
In some ways, it's hard not to agree with the many unfair things about Tattycoram's situation that Miss Wade points out. The Meagleses did give her a crazy name that marks her as different, and the whole we'll-adopt-you-to-become-our-servant thing is kind of questionable. (Although back then, it's way better than whatever horrors Tattycoram would have been exposed to at the orphanage.)
On the other hand, like many of the novel's doubles and shadow characters, Tattycoram seems to be a symbolic acting-out of whatever unseemly emotions Pet might have. Since she is already a social pariah, Tattycoram gets to be angry and bitter and miserable about her life, unlike Pet, who is responsible for much of her parents' happiness and so tends to remain super chipper. Tattycoram also gets a real escape from this life – not the polite kind of escape that Pet talks about when she tells Arthur why she's getting married, but an actual destructive rampage of running away.