As we have no evidence of how the children behave when with their mother ..there is no evidence to back your claim.. But we do have regular evidence of how their father allows them to behave when with him
We do also have evidence of how their mother allows them to behave also, due to her TV show.
On peters and Katie's show we have also witness him telling the children off, eg: princes throwing a strop, Junior disappearing to play with IPad and he showed good parental skills. Katie showing good parental skills with Harvey, when he refuses to do something or when he throws a strop.
Peter and Katie seem to be good parents. Judge the adults behaviour not the children. The children are typical of most children behaviour.