Probably Theory of the Firm. It's part of micro theory and deals heavily with principle-agent models. In the context of parenting, you and your wife are the principles and your kids are the agents. These models cover how the principle should structure incentives so that the agent will do what the principle wants. Appropriate incentives can vary widely depending on the situation.

There are some great books about parenting specifically, though.

I haven't finished The Family Firm, yet, but Emily's other two books are great resources for people just starting a family or with very young kids.

Bryan's book is a bit more technical, but I think it has the more profound message.