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I always got the impression that Norman in his wife were divorced.
I mean, clearly his wife moved to hoenn to let her child be closer to their dad, but she moved an entire two cities away from him. They always refer to the other as "your mom" and "your dad" but never say "my wife/husband." also the only time they are seen together is at the very end of the game, after their child won the championship, which is kind of like when both of your parents go to your graduation, willing to briefly put aside their differences for their child.