Is it permissible for one who divorced his wife a third time—knowing that what happened was a trick to bring about the divorce—to take her back, and does what happened fall under what is known as "istirʿāʾ" (making one a shepherd or guardian)?

Your divorce of your wife when her father requested it is an actual divorce, and the absence of intention does not harm it, because an explicit divorce does not require intention. This is not a case of coercion due to the lack of its conditions. The other two divorces are also actual, and psychological or physical pressures do not prevent their occurrence and are not considered coercion.