Dear A.,
Not knowing why your daughter was sent to her room and why she became so upset as to choke the cat, my response is not meant to scare you.
However, it is something to consider.
It is possible that your daughter has been touched in an inappropriate way and is acting out. Someone may have controlled her into a very frightening position and threatened her. If this has happened, the person, or people involved may have told her that if she said anything, her family would be hurt.
I would sit down with her and have the kitten on your lap. Explain that the kitty is just little and cannot defend herself. Ask her gently why she choked the kitten and if she understands why it is wrong to do that. Explain the kitten could have been hurt very badly. Let her know how proud you are of her that she told you about the choking and that it was the right thing to do because the kitten is an animal and can't tell such things whereas people can. This may encourager her to open up.
I hope this helps.
M. C S
I am a divorced grandmother of 62.