Am I subject to the prescribed punishment of stoning or execution for hearing insults against religion and the Prophet (peace be upon him), and my attempt not to laugh, and my imagining the reaction of the one who uttered the insults, and to what extent does my obsessive whispering affect the ruling of disbelief?

Intense fear of God's wrath indicates faith. As for someone who doubts that he laughed, the default is that he did not laugh, because certainty is not removed by doubt. And whoever commits an act of disbelief should not impose the hadd punishment upon himself; hudud punishments are for the ruler to administer.

As for the man who insulted religion, this is a serious matter. He must be advised and warned about God. If he repents, then praise be to God. Otherwise, shunning him is required, but subject to what serves the greater good.

As for his daughter's laughter at that moment, it indicates a lack of zeal for religion. This was a moment of anger for Allah Almighty, not a moment for laughter. Aisha (may Allah be pleased with her) used to say: "The Messenger of Allah (peace and blessings be upon him) never took revenge for himself for anything done to him, unless the sacred limits of Allah were violated, in which case he would take revenge for Allah."