Nick Reiner

As we reported ... the couple was found by one of their daughters Sunday with their throats slit inside their Los Angeles home. LAPD Chief Jim McDonnell said Nick is a suspect in the case, and announced his arrest on suspicion of murder.

Rob Reiner and his son Nick were on rocky ground long before tragedy struck ... with both publicly hinting at a fractured father-son relationship years before the director and his wife were brutally killed ... crimes Nick is now allegedly linked to.