Familial relationships are an important theme in The Taming of the Shrew. Aside from the obvious husband-wife relations, the play also portrays tumultuous father-daughter bonds, sibling rivalry, and power struggles between fathers and sons. As a comedy, the play seems to be outwardly working toward the reunification of the family, and it's true that by the end, order seems to have been restored. Yet, Shrew also leaves open the possibility that all is not well. Kate and Bianca never come to terms as siblings, fathers seem to forgive their children a bit too easily, and we're not quite sure what will happen off-stage when married couples return to the privacy of their own homes.
In The Taming of the Shrew the typical hierarchy of families is subverted and then reestablished by the end of the play.
The Taming of the Shrew would be a completely different play if Shakespeare had given Kate and Bianca a mother.