Molyneux put Stanley in front with a fourth-minute free kick against League Two leaders Chesterfield, for whom Cook is manager with Richardson joining him as assistant in the summer.
Molyneux then doubled the lead five minutes later as he scored from the rebound after Danny Webber's penalty had been saved, following a foul by Ritchie Humphreys on Will Hatfield.
Stanley were reduced to 10 men after 32 minutes when Peter Murphy was sent off for a second bookable offence, but they led 3-0 at the interval as Molyneux completed his hat-trick in the 45th minute.
Cook was then sent from the touchline together with Stanley assistant manager Paul Stephenson following a row over a tackle from Chesterfield's Ollie Banks on James Gray on the stroke of half time.
The visitors pulled a goal back through defender Ian Evatt with five minutes left but Stanley had already done enough to secure victory and move six points clear of the relegation zone - even if they remain third bottom in the table.
The Reds also handed a debut to right back Adam Buxton, who joined on a month's loan from Wigan on the day of the game as cover for the suspended Nicky Hunt.
Stanley: Marcus Bettinelli, Adam Buxton (Rob Atkinson 70), Dean Winnard, Tom Aldred, Laurence Wilson, Will Hatfield, Peter Murphy, Luke Joyce, Lee Molyneux, James Gray (Kayode Odejayi 70), Danny Webber (Josh Windass 46). Subs not used: Andrew Dawber, Kal Naismith, Max Hazeldine, George Bowerman.