The kingdom of Christ is already in this world, though not of it. That kingdom is two-fold, perfect in heaven, imperfect on earth. We pray that God's kingdom of grace may be extended in the souls of men, and that they may so fulfill the will of God that they may attain that final happiness of the kingdom of heaven. But the words you quote in no way refer to another temporary state, or to any second chance.
When Christ comes again it will be to judge mankind, not to teach and rule us in this world. He has put His Church on earth to do the teaching, and if men will not listen it is their own fault. Now is the time of our probation and we must make good use of the present life instead of relying upon future opportunities for preparation.
That has no reference to a further probation on this earth. The thousand years are to be interpreted in the Hebrew sense of a long and indefinite period of time. Even to-day we say, "I could listen to such music for a week," without intending precisely seven days. The thousand years refer to the long period between the advent of Christ and the end of the world. The supply of grace is more plentiful and God's mercy more copious, so that Satan's power is truly diminished. And those who, for the love of Christ, have learned to rise above things of earth and live for God truly reign with Christ.
The first resurrection is the mystical resurrection from the death of sin. We rise with Christ in Baptism, and those who die still retaining the grace of their baptismal rebirth possess a permanent title to the glorious second and actual resurrection of the body at the last day. On such as these the second death will have no effect. The first death is the dissolution of soul and body. The second death is the eternal living death of hell.