Did you know that Economics and Politics etymology senses are related? A definition of oïkonomia (economy) would be the organization of the house while one of Politikos (politics) would be the study of a city's organization, of social interactions, and the use of power to regulate it. Politics would be Economics but on a bigger scale!

If economics and political science turn out to be two sides of the same coin, why not just put them both in one department?

Obviously the two fields overlap. Politics define the rules adopted to make the economic wheel works a certain way. Economics are the rules that make the economic wheel works. The main difference here is that political science intent to make the economy works according to a vision, to beliefs and though, to people. There is this notion of power in action to organize the state, just like you organize your home. In a way, political economics is the study of the economical rules that make people live peacefully together.

I would say that economics are the maths, while politics are philosophy. You discover the rules and think about how to apply it according to your vision.
Now, I don't think Political Science and Economics should be put in the same departments since they are not dependant. You can do economics without thinking of political sciences. In the same way, you can study political sciences from a geopolitical perspective, or a psychological one.