Is it permissible for the husband's father to wake his household for Fajr prayer in a terrifying manner (by banging on iron doors) when there are young children present?

It is permissible for your husband's father to wake you up for Fajr prayer, especially if time is running out. This is obligatory according to some scholars and recommended according to others. You should praise his action and thank him for alerting you to the prayer and for his diligence in that regard. If his method of waking you causes distress to you or your children, gently advise him and agree with him on a quieter method, such as a phone call. If this method is unavoidable, it is better than missing the prayer, and knocking on the door does not cause significant harm to children. It is advised to magnify the importance of prayer and prioritize it above all else.