If a nation launches a nuclear weapon that causes major destruction, does the targeted nation have a right to respond in a way that virtually obliterates that nation?

The simple answer to your question would be no. The targeted nation could not simply retaliate in kind, and certainly not seek to obliterate the offending nation. 
 
Some sort of military response might well be called for, even full-scale war. This would presume that the criteria for just war have been met. Namely, that the damage and threat was grave, lasting and certain (which would be the case in your scenario), that other means of ending the conflict has been tried or were not possible, that there is a reasonable hope of success in turning back the threat by military means, and the use of arms must not produce evils and disorders graver than the evil to be eliminated (cf Catechism #2309). 
 
Even once within a war, a nation must use means to distinguish between combatants and noncombatants. Hence, choosing to wipe out whole population centers, indiscriminately killing combatants and noncombatants, is not a moral option. Indiscriminate obliteration cannot be condoned under any circumstances. (cf Catechism #2314). 
 
It will be admitted, given the existence of large-scale nuclear devices, the most effective means to deter such attacks is complex and debatable. A short answer such as this cannot possibly explore all the points debated in the deterrence of nuclear threat. Simply here let it be noted that the Catechism expresses strong moral reservations regarding the modern “arms race” (cf Catechism #2315). 
 
Thus, to return to the main question, if a nation were lamentably to be attacked by a country in the way you describe, that nation is not thereby justified in indiscriminately retaliating by wiping out whole cities or in annihilating that country.