Could it mean that their son will be born on September 3? The following sentence is 'we are excited but life will be tough'.
Sure! The following sentence makes me understand more about what really goes on in your family. Some people like me may get the wrong meaning just by reading your first sentence. If someone tells me "We're expecting our son to join the family on 3 September., I would think that your son may be a teenager or adult who is returning home from college or other town.