I spent a month in Guatemala a couple of years ago, and there's good infrastructure for volunteering there. Finding a place where you could get room and board (especially for all of you) in exchange for volunteering might be difficult as resources are so very limited, but Guatemala is an inexpensive country. The people are so lovely and are very welcoming to American children (adults too, of course). Do you speak Spanish? If you don't, you'll find that most places won't be interested in working with you until you do--you could spend the first month or so in Spanish classes and then start volunteering.
The school I attended will set nurses up with a midwifery clinic in another town: http://www.spanishschools.biz
. Other schools will do this, too. Then there is this place: Hospitalito Atitlan