Learn English – A word or idiom to describe an abusive parent who wants to keep their child

I just finished watching the video game Among the Sleep and at the end

(SPOILER ALERT) the mother is the abusive one.

At the beginning of the game, the mother seems to cling onto the child possibly in memory of the little boy's father. At the end though, the father comes and takes care of the baby. I want a word or idiom to describe how the mother is attached to the baby—maybe as a way to get to the father—but who doesn't show any real love to the infant.