I suspect that there is no equivalent thing in Western culture, hence no convenient word in English.
Maybe you have to simply explain the cultural idiom in whatever words it needs.
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Mr Google says
How can I translate "Chicken Baby"? English
Chicken baby is a verb that means educating children, teaching children, and counseling children. In order to prepare for some kind of exam.
Cram school?
Sending them to cram school.
Tiger Mom'ing them?