In the book Griet has a younger brother and sister. By the end of the book, the brother has run away from Delft because, having become an apprentice tile painter, he hates the work and doesn't want to follow in his father's career path; and the sister has died.
The tile shows a boy and a girl who are supposed to be Griet and her brother. For Griet, who has had to leave home to work, it evokes memories of when her family was together and not desperately poor. When Cornelia breaks the tile, it's a fresh reminder to Griet that her family is broken: her sister dead, she and her brother gone away to find work.
Without the brother and sister in the movie to provide context, there's almost no point in even having any scenes with the tile, except to show Cornelia being bratty again.
There is no implication that Griet's father painted the Vermeers' tiles. The book even says that Griet looks for tiles painted by her father but doesn't see any.
The tiles don't symbolize anything. They have a practical purpose: so that when the housewife or maid mops the floor, the water won't damage the paint on the walls.