It certainly appears that you interpreted this dream correctly. I hope this is true and that it does happen.
However, Mr.Trump may be able to achieve something great (as you mentioned) without becoming president again. What if he can prove that he was supposed to be president, that he in fact did win the election? In that case, everybody will know that the presidency was rightfully his.
What if this is not about the presidency but about another way or “vehicle” that puts him in a powerful position to control and change things?
However, I must admit, based on the symbols in the dream and the meanings that you described, there is a good chance that you are right about him being president again.