Is it permissible to allow one's wife, along with their son, who is a year and a half old, to travel to America to visit her married sister and brother there?

A woman is not permitted to travel without a mahram, and the prohibition is even greater if the travel is to non-Muslim countries due to the moral decadence prevalent there. The prophetic hadiths affirm this, regardless of whether the journey is long or short, as anything considered travel is forbidden for a woman without a husband or a mahram. Scholars have reached a consensus on the impermissibility of a woman traveling without a mahram, except for Hajj and Umrah, or exiting from the land of shirk, or fleeing from captivity. A young child is not considered a mahram; rather, the mahram must be an adult of sound mind to be able to protect the woman.