First of all I must say I am surprised you've never traveled outside of the US (even tho you've mentioned it before). That will without doubt be some great experiences for you. Travel programs on TV can't even give you a fraction of what your senses will absorb when you're actually there in the middle of Ulan Bator, Karachi or where ever you choose to go.
Anyway I second Marina in taking a nanny with you. In my opinion that's the best solution when the children are that young – at least for the three years old. I think they will benefit tremendously from experiencing foreign cultures that early in life. And that goes especially for the older one who probably can grasp more than the younger one.
Happy traveling!
Espen