I think you're missing the point. The idea of Mutually Assured Destruction is precisely why the Capitol didn't use nukes in the first war.
During the Dark Days, the rebels in 13 wrested control from the government forces, trained their nuclear missiles on the Capitol, and then struck a bargain: They would play dead in exchange for being left alone. The Capitol had another nuclear arsenal out west, but it couldn't attack 13 without certain retaliation. It was forced to accept 13's deal. The Capitol demolished the visible remains of the district and cut off all access from the outside. Perhaps the Capitol's leaders thought that, without help, 13 would die off on its own. It almost did a few times, but it always managed to pull through due to strict sharing of resources, strenuous discipline, and constant vigilance against any further attacks from the Capitol.
-- Mockingjay, chapter 2 (emphasis mine)
Mutually Assured Destruction ("if you attack us, we both die") is the exact concept being referred to here. The Capitol didn't nuke Thirteen because of MAD - that's why Thirteen was allowed to survive. In short, the answer to your question is:
How could the Capitol use nuclear weapons against District 13 provided that “Mutual Assured Destruction” doctrine was in place?
They didn't, and precisely for this reason.
