Yes, both officially, and unofficially she did find execution not something she wanted. Was it not Empress Elizabeth who abolished the formal death penalty in Russia? At least, I thought she did.But, Catherine like to look enlightened, not like some Russian despot. She didn't want the monarchs she liked to look enlightened to in the western world to think she would order the execution of her husband, to make way for her to have the throne. Nor did she want the world to speculate about the mysterious death of her son and heir, which would have aroused quite a bit of attention, because he was the heir, and she was widely known. Her husband people already knew was a fool, and he had worn out his welcome, so people were less inclined to pay attention to his mysterious death. I think she might not have done anything to her son because she knew how his ''mysterious'' death would look.