And then I think she became to SD a second chance to get the life SD herself wanted to have, second hand

I was actually going to say, it's really telling when Wilhelmine says that the English marriage project would be a perfect fit for her *mother*, but not for her at all. And it is super common for abusive or even emotionally neglectful parents to live vicariously through their children, which it's pretty clear SD is doing here. It's also probably how SD justified her verbal abuse (which she wouldn't have seen as such): she's trying to give her child the best life possible, so why is child so ungrateful??

Along with cahn, I'm inclined to cut SD a tiny bit of slack, given that

1) Wilhelmine says she was straight out lying to her mother about where all the injuries were coming from.
2) My impression of the social dynamics is that servants have a whole separate grapevine amongst themselves, in which people like SD are not supposed to participate. Even if a governess is a step above, say, a parlormaid, there's still a communication divide. So a fellow governess might pick up on abuse first.

But yeah, it's not great, and SD is far from blameless in this episode.