Without putting too fine a point on it you're doing it wrong.
Don't connect the second Airport to the router. Instead use Airport Utility to get the second Airport to join the existing wireless network.
What's happening in your case is that the two Airports are conflicting with each other as the default IP Address ranges will be the same.
By joining the second Airport to the existing Airport network you aren't providing an extra IP Address range you are in fact simply boosting the range of the current one and using that one's IP Address range.