There were wire hangers in the house cuz that brat Christina put them there. She deliberately broke the rule!
The punishment was excessive though. Beating a child with a wire hanger is abuse tbh. I doubt that ever happened anyway. It just seems not to fit. Ya know?

In the book, Christina explains that when the dry cleaning came back, it was the kids' responsibility to change the clothes to the correct hangers. Christina just failed to do so.
groovydoom.blogspot.com

I think the thing that bugs me every time I see this is why she went after Christina, she didn't do it! But she was obviously wasted
"People who live within their means suffer from a lack of imagination" Oscar Wilde

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It's not really a plot hole. Obviously, the hangers came from the cleaners, and they got passed somebody and wound up in Christina's closet.
But the mother is abusive fundamentally, especially when drunk, so her motives aren't rational.

sigh<
so the wire hanger incident was supposed to represent the many night raids that Christina and Christopher [notice how it is only those two] had to endure. The wire hanger had somehow gotten inside the house although it looked like it was better made than the average wire hangers you'd get from the dry cleaners.
It was meant to represent how quickly mommie would go off and what would set her off.
nothing more.
Oh God. Fortune
vomits
on my eiderdown once more.

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The laundry company and dry cleaners to which Joan entrusted the family's clothes were under strict instructions to return all clothing on the covered hangers that she provided. Now I suppose it's possible that on one occasion the company failed to do this and it triggered Joan's irrational outburst. But it was the job of the housekeeper to make sure the clothes were returned to the wardrobes after these deliveries and it would have been her head or job if this instruction was not carried out.