Is
it true that a father should not kiss his daughter on the mouth and that a
mother should not kiss her son on the mouth?

Praise be to Allaah. 

This
is true. A man should not kiss his mother or daughter on the mouth.
Similarly, a brother should not kiss his sister on the mouth, or his
paternal aunt or his maternal aunt, or any of his mahrams. Kissing on the
mouth is only for husband and wife. And Allaah knows best.