As written, it is way too complicated. Consider this: "Since he could not achieve his dream, he is living vicariously through his son." Or you can reverse the clauses and have the same meaning. You can make it simpler and say: He is living vicariously through his son. The meaning is understood.

The sentence sounds unnecessarily long and convoluted to me. I would say it more simply? For example, I doubt these shorter versions change the meaning much. 1. Unable to fulfill his dream himself, he tries to realize it through his son. 2. (After) Failing to do it himself, he is trying to realize his dream through his son. 3. After failing in his own turn, he tries to make his dream come true through his son.

Hi belle H, I suggested that you swap the verbs "carry out" and "fulfill" because English speakers, like other speakers, we Italians included, love coupling words in kinda fixed formulas, and I heard "to fulfill a dream" a lot of times, for instance in the wonderful song by Elvis Presley: "love meeee...tendeeeer... love me truuue...alllll...my dreammms...fulfillllld..." https://www.youtube.com/watch?v=Txh5l7cQXa0 "fulfilling a dream", these two words sound so well together!

I would say: "since he could not carry out his achievement, he tries to fulfill his unfulfilled dream through his son". Note "through" instead of "though".