Stuart, 38, had reportedly run the light on Avoca street in Randwick, a short distance from the couples home - at about 4pm in the afternoon.
Soon after, it's reported that the coach of the NSW Helensburgh Tigers football team was also allegedly driving on a suspended licence.
Stuart has been charged with mid-range drink driving and his licence has been cancelled, it's reported.
If convicted, the former Sydney Roosters player will face a further six month licence suspension.
Stuart and Kate, 40, married in 2010 and share a daughter Mae, born in 2014.
Stuart is expected to appear in front of Waverley Local Court in April 2019.
