What is the ruling on casting the pebbles on behalf of one's pregnant wife who is not present during the stoning of the Jamarat?

It is permissible for the husband to stone on behalf of his wife if she has a valid excuse, such as if stoning would cause her extreme difficulty or if there is a fear of harm to her fetus. Her presence at the stoning site is not required. Otherwise, it is not permissible, and she must offer a sacrifice (dam). As for her not spending the night in Mina, if she has no valid excuse, she must offer a mudd of food according to the Shafi'i school, and a sacrifice (dam) according to the Maliki school, with the relied-upon opinion being that of the Shafi'i. If she has a valid excuse, there is nothing upon her. Regarding spending the night on the third day of Tashreeq, it was not obligatory for your wife because she departed before sunset on the second day of Tashreeq.