The/A mountain of family responsibilities had already descended in/on her head.
According to me, it is in her head.
But I am not 100% sure about the answer because in the net various answers are given.
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On for the sentence as written.
Reason: “Descend in” implies that the problems are already in her head and are moving. I think you mean that the problems are coming to her and collecting in her head. If you want to emphasize that the problems are in her head, I suggest
...already accumulated in her head.
or, if you want to keep “descended”
...already descended into her head.