[under one's thumb] or [under the thumb] {adj.}
or {adv. phr.}
Obedient to you; controlled by you; under your power.
* /The Jones family is under the thumb of the mother./* /Jack is a bully. He keeps all the younger children under his thumb./* /The mayor is so popular that he has the whole town under his thumb./
Compare: JUMP THROUGH THE HOOP.