We could start with the fact that even the President cannot operate the "football" on his own. Any use of nuclear weapons requires the approval of the Secretary of Defense. At no stage, from POTUS to the people who would launch can anyone do it alone.
You make an excellent point about Hillary in that she campaigned on the idea of establishing "no-fly zones" in Syria, which would have required our military to shoot down Russian planes. Silence from her supporters.
How would Americans feel if Trump made agreements with North Korea which allowed us to withdraw troops and equipment from the Korean peninsula so that we could use the money for more critical issues like repairing our infrastructure?