Two bodies is an assumption. By the way, it is not a secret gathering. It just that the event takes place in an amount of time that can't be divided. For all we know, at the time that the gathering takes place, an unbeliever could be having a conversation with his friend who is a Christian an see him disappear right before his eyes.
We can't just make up our own understanding of this, but we need to look at all related scriptures in order to come to a right conclusion. That fact there is no mention of two bodies is neither mentioned nor fits Jesus resurrection, which is our example. Jesus resurrected in the same body that He was crucified in, but immortal and glorified. It will be the same for all believers. The only difference is that, those who are still alive, because they are not dead, will just be changed immortal and glorified. Those who are alive at the time that the resurrection takes place will not experience physical death, but will be changed where they stand.
Your whole response here is about the believers, resurrection, and the living being caught up, your proclaimed (Pre-Trib) rapture.
Is what you "Fail" to reveal is Gods clear words on the timing of this event, as the resurrection of the believer takes place on "The Last Day" not any time before it.
1 These 4:14-17KJV
14 For if we believe that Jesus died and rose again, even so them also which sleep in Jesus will God bring with him.
15 For this we say unto you by the word of the Lord, that we which are alive and remain unto the coming of the Lord shall not prevent them which are asleep.
16 For
the Lord himself shall descend from heaven with a shout, with the voice of the archangel, and with the trump of God: and
the dead in Christ shall rise first:
17 Then we which are alive and remain shall be caught up together with them in the clouds, to meet the Lord in the air: and so shall we ever be with the Lord.
John 6:40KJV
40 And this is the will of him that sent me, that every one which seeth the Son, and believeth on him, may have everlasting life: and
I will raise him up at the last day.
John 11:23-24KJV
23 Jesus saith unto her, Thy brother shall rise again.
24 Martha saith unto him, I know that he shall rise again
in the resurrection at the last day.