This would make Jesus' prophecy not only unable to be properly understood, but to be actually misleading in the day He gave it.
Do you somehow not know that until they received the Holy Spirit there were a lot of things that the disciples did not yet understand? Jesus knew that they would not understand everything He was saying at that time. That's why He said this...
John 14:26 But the Comforter, which is the Holy Ghost, whom the Father will send in my name, he shall teach you all things, and bring all things to your remembrance, whatsoever I have said unto you.
They likely did not know at the time He was speaking that the elect would include Gentiles, but they certainly understood that after the Holy Spirit taught them "all things".
Paul very clearly taught that the elect include all Christians (Romans 8:31-34). Therefore, the elect that will be gathered when Jesus comes will include all believers, Jew and Gentile.
The elect are gathered before He takes His throne, the nations after.
Wrong. It does not say that. What it actually says is that all nations (Greek: ethnos - people) will be gathered before Him after He sits on His throne. That does not mean they are not gathered at all until then. It means that they are not yet brought before His throne until He sits on His throne. They would already have been gathered before that, but not yet before the throne. So, the elect will be gathered and then after that will join the non-elect (unbelievers) before His throne, after which they will be separated to His right hand and left hand.
The elect are gathered in a group, the nations are gathered in a separate group, and are then separated according to how they treated Jesus' brothers, the Israelites.
That is not at all what the text says. You are reading things into the text that aren't there. Jesus's brothers are not the Israelites. This is once again a case of you interpreting scripture without taking other scripture into account. Here are who Jesus Himself said His brothers are...
Matthew 12:47 Then one said unto him, Behold, thy mother and thy brethren stand without, desiring to speak with thee. 48 But he answered and said unto him that told him, Who is my mother? and who are my brethren? 49 And he stretched forth his hand toward his disciples, and said, Behold my mother and my brethren! 50
For whosoever shall do the will of my Father which is in heaven, the same is my brother, and sister, and mother.
There it is. Jesus did NOT say His brothers are Israelites. He said His brothers are those who do the will of God the Father. Christians are those who do the will of the Father by following Jesus. You are trying to add a third group that isn't there. There are only two groups. The sheep and the goats. The least of these refer to sheep/believers who were hungry, thirsty, sick, in prison, etc.
Gentiles are divided sheep and goat according to how they treated Jesus' brothers, the elect, the chosen nation, the not-gentiles, Israel.
Christ's sheep include both Jew and Gentile believers, as John 10 shows. You are not using scripture to interpret scripture here.