I feel that Bradbury's significance in the depiction of the relationship between children and parents is one whereby there is an abdication of connection bonds between one another.  To an extent, the parents have abdicated their connection to the children with the advent of technology.  This results in the children abdicating their responsibility to their parents in deference to the technology.  The only emotional bonds that the children have are to the room and to technology.  The significance here is that Bradbury has constructed a reality whereby the modern setting has lost emotional connection to one another.  There is only a connection to technology.  This bond is to the point where the children sacrifice with ease their parents.  The significance of this relationship is one in which the traditional notion of connection and loyalty is severed.  This new construction is one in which technological advances have created a dependency whereby emotional connection to other people have become transformed into an intimately frigid realm.  This helps to highlight the condition of the future that Bradbury wants to accentuate.