How can I find a great intention in sitting with family, and how did the Messenger of Allah, peace and blessings be upon him, balance spending time with his family and the three purposes for which Allah created us: worship, good character, and building up the earth?

A Muslim's sitting with his family and socializing with them is a permissible and legislated matter, which the Prophet, peace and blessings be upon him, affirmed. Indeed, it becomes an act of worship if one intends by it to bring joy to them, and it becomes a means to invite them [to Islam] and teach them good. The Prophet, peace and blessings be upon him, used to sit with his family and assist them.

The time allocated for this is not fixed; it should be according to what is possible. The important thing is that this sitting does not distract one from what is more important, which is the worship of Allah.

As for criticizing others and seeking out their faults, this is a serious matter that the Prophet, peace and blessings be upon him, forbade.