What is the connection between parenting and discipleship? Don't parents have enough on their plates to do already? Why would they take on discipleship, too? Isn't that job best left to pastors?

Not at all! In fact, discipleship goes hand in hand with the Christian view of parenting. It's not an extra thing to add on top of parenting, but more like the way one approaches parenting. 

Parent's are actually the best suited, the best equipped, and the ones called by God to be the primary disciple-ers for their children!