My question is: If a man dies, the marriage and children of that marriage are sealed in the temple, the wife re-marries, but is unable to be sealed to the second husband (correct?) who is also a worthy recommend holder, if there are children of this second marriage, who will these children belong to after this life?
As you indicate, a woman who has been sealed to one person may, after that person’s death, be married again to another–but that second marriage is for time only, and that union is dissolved at the death of either partner. The family unit exists as such in the eternities only in the condition of exaltation in the celestial kingdom. So, since the second marriage in this case does not exist after mortality, the children cannot belong to the second husband. However, having been born to the woman, who remains faithful to her covenants, it would be expected that the children of the second marriage would belong to their mother and to her eternal companion.