I think "My son can't join this faculty." can also refer to the future, right? If so, we can use "could join", what do you say?
You are talking about this father's hope in the future. It is something that he is willing to happen one day.
1. I wish my son would join the faculty of Engineering. (This is my hope, but I don't know if he wants to.)
2. I wish my son could join the faculty of Engineering. (It implies that he doesn't have the ability to join this faculty or that it is not possible for him to join this faculty. In either case, the meaning will contradict with 'hope' which indicates that you want something to happen as you believe it is likely or possible.)