Pence will not try to nuke a country because someone made a mean Tweet. Can you say the same of Trump, who reportedly asked repeatedly why he just can't nuke someone during his first briefing as a president?
Unofficial rumours do say that Mattis has people near Trump to stop him, one way or another, from launching an attack but those are just unverified rumours and even if true, that's all kinds of fucked up as well.
Nearly no one wants to restart the Korean war. All the countries would just be harmed by it. Senseless slaughter and suffering would follow and the money spent in the war would offer little profits.
Tough talk is standard practise. Negotiations and sanctions are standard practise. Trump on the other hand joins Kim in the "dictator dick measuring contest" quite earnestly which will just further destabilize the situation.
EDIT:
http://thefreethoughtproject.com/trump-killed-more-civilians-obama/Trump has managed to beat Obama in at least one category now... Killing civilians.
Which, to be fair, was one of his campaign promises. He said he would kill the families of the terrorists, and by God, he certainly seems to be doing his best in that endeavour.