I do something similar to this, though I'm single, no kids.
Most people on the thread have already pointed out the various benefits and complexities, money wise, but do think of the social cost, too: while I love to travel and live abroad, the number one thing I miss is my community of friends and family back 'home'. When you move around a lot, you don't have the time to make real connections, and it gets pretty lonely. Particularly with a young kid, you might miss the community of friends/parents, etc.
To practicalities: Definitely verify the living expenses before going; 'poor' countries can be surprisingly expensive! Also, make sure you choose a place with good public transit or biking options cause buying and reselling vehicles would be a major pain.
One thing to keep in mind is health insurance: will your current policy work abroad if you're out of the states for long periods of time? Check on this and, if not, do cost crunching on the alternatives….