Although many of the twelve tribes of Jacob may be traced amongst the Yehudy today, does this represent the fulfilment of the prophecy of the joining of the two sticks at the end times?

Shalom. As is often the case, prophecies are open to several different interpretations of the classic commentaries, which may all be correct either simultaneously or perhaps at different stages in Jewish history. For example, the Abravanel explains that the mentioned prophecy of redemption (Ezek. 37) refers to the future unity in the end of days, where we will no longer be divided into two or more kingdoms or tribes, but will be one united nation under one united flag. In fact our rabbis differ in the Talmud whether the lost ten tribes will return at all. Others explain that the physical or national redemption [represented by Joseph/Israel which was, after the split of the kingdoms, physically (militarily, economically and numerically) the stronger of the two], will precede the spiritual rejuvenation (represented by Judah which was generally more religious), and will serve as the base upon which the latter will be grafted. Just as when grafting two trees, the idea is to benefit from the stronger traits of each of the two different trees, similarly, the ideal future kingdom of Israel will be strong both nationally and spiritually.