"In that day they will say, 'Surely this is our God; we trusted in him, and he saved us. This is the Lord, we trusted in him; let us rejoice and be glad in his salvation.'" NIV translation
The people of God will sing and dance for joy as they celebrate the day that they had waited on for many years. They will rejoice in the fact that God has removed the shame from His people.
"The hand of the Lord will rest on this mountain; but Moab will be trampled in their land as straw is trampled down in manure. They will stretch out their hands in it, as swimmers stretch out their hands to swim. God will bring down their pride despite the cleverness of their hands. He will bring down your high fortified walls and lay them low; he will bring them down to the ground to the very dust." NIV translation
This period of time (Millennial Reign) will be a time of separating as well as uniting. The NIV translation is not as good with this passage as it gives the impression that the Moabites are swimming but that is not really accurate. The passage speaks of the hand of God parting the Moabites from His people much like a swimmer parts the water with an open hand.
So, why is God parting the Moabites and who do they represent? We see the answer to the question of why in Deuteronomy 23 as God declared that they would be excluded from the assembly of His people.
This was because of the fact that they had attempted to hire Balaam to curse God's people. Here, they are representative of all of the people of the earth that are enemies of Jesus Christ and His people. Who are the enemies of Jesus Christ? All of those who deny the fact that He is the Son of God who takes away the sin of the world.
Those who have placed their trust in Jesus Christ will be united with fellow believers in celebration. Meanwhile, those that reject Him will be prepared for the final judgment which is separation and Hell.