You want Bush, or any American leader, to work with Hezbollah (funded by Iran)?

In Iraq, the US works together with Da'wa and SCIRI.

I just don't see how that would work

I suppose you're right: it isn't working in Iraq either.

Is there a non-militant Hezbollah wing?

I don't know about "non-militant", but "non-military" there is. Like Hamas or the Muslim Brotherhood, the reason these organizations are successful is that they provide the social services that our friendly dictators don't provide.

I just haven't heard of one

I suppose you haven't been listening to the right sources. Try wikipedia for a start.

The civilian wing of Hezbollah runs hospitals, news services, and educational facilities and participates in the Lebanese Parliament. Its Reconstruction Campaign (Jihad al-Bina) is responsible for numerous economic and infrastructural development projects in Shia-populated areas of Lebanon.

Nothing is 'mere'. — Richard P. Feynman