Does one whose indirect distress – such as distress concerning one's children – fall under the virtue of alleviating hardships when one consistently seeks forgiveness and recites abundant prayers upon the Prophet, hoping for God's reward?

The necessity of seeking forgiveness, increasing acts of obedience, sending blessings upon the Prophet (peace be upon him), and reciting the Quran—through these, Allah will relieve anxiety and remove distress. This includes the removal of anxiety and distress from children and spouses. If one is concerned about their children, then their distress is part of their own distress, and their anxiety is part of their own anxiety. Therefore, one may supplicate to Allah through righteous deeds for their distress to be removed. Allah may indeed lift the affliction from them, and He may inspire the person with patience and seeking reward from Allah, and expand their chest.