Does excessive imagining of the torment of the Hereafter, out of fear of it, lead to having a poor opinion of Allah? Is this action correct? And which is better: praying at home with one's wife and children, or in the mosque?

Your dedication to your children and your efforts in providing for them are acts of worship. It is important to balance your duties, giving each their due right: your family, your Lord, and yourself. One who is journeying towards Allah should proceed between fear and hope, and not allow fear to overcome them to the point of despair. Regarding the institute, choose what is most beneficial for you: attending while avoiding temptations, or staying at home. The obligation of congregational prayer is lifted by your prayer with your wife. Speak to your wife with gentleness and kindness, and invite her to cooperate and be patient.