All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
You are not obliged to do anything towards the son of your wife, however, if you do good to him, then you will be rewarded for it as he is the son of your wife; Allaah Says (what means): {And do good; indeed, Allaah Loves the doers of good.}[Quran 2:195] Allaah also Says (what means): {Indeed, Allaah Does not Allow to be lost the reward of the doers of good.}[Quran 9:120]
In principle, a wife is obliged to obey her husband and reside where he resides, so you have the right to ask her to come to reside with you in Saudi Arabia. However, it seems that you do not wish to oblige her to do so; rather, you want to reach a solution whereby you achieve your benefit on the one hand, and the benefit of your wife and her son on the other hand. Hence, we advise you to seek the advice of rational and trustworthy people around you who know your circumstances, because the one who seeks the advice of the people and performs the Istikhaarah prayer will never be unsuccessful.
It is appropriate here to suggest to you the following solutions:
1- To bring your wife and her child to reside with you, and endeavour to find a way for the child to continue his studies in Saudi Arabia or in your country through correspondence.
2- To marry another wife who will be with you in Saudi Arabia and your present wife will stay with her son and you will go back to them whenever possible.
3- To let you wife continue the same program with you, in a way that she comes to you in Saudi Arabia and stays with you for a period of time, and then she goes back to India.
Allaah Knows best.