My ancestors traveled back and forth across the Atlantic, having babies on both continents. I don't know if they owned homes in both countries, but they popped up on the census records of both countries. Since it's unlikely that the census was taken on the same day/month in both countries, it's very possible to appear on both countries' census records.
I've found cousins being born within a month of each other, each named James, registered in the same quarter in the same registration district and the same town, and children of fathers bearing the same names. Very, very difficult to figure those families out. You might have the same situation.
If you haven't already, why don't you post the details you do have on the pertinent location boards. Perhaps someone with local knowledge can help you figure out the puzzle.
Good luck!