Witness 007: Without major diplomatic efforts involving China the NK nuclear program is unstoppable; it is important to emphasize they have nuclear weapons it is just a matter of easier delivery at this point.
Unfortunately, there is no good military option against NK, which is why the bluster about red lines and first strikes makes little sense. According to current planning (the stuff which is publically accessible; interesting reading BTW), NK would be defeated, mainly because their equipment is old and their stockpile of weapons and fuel is not very deep, but it would be at a very great loss to South Korea.
On top of that comes two great unknowns. The first is that NK and China are in a military alliance such that hostile action against NK would put the US and China at war legally(!). Nobody knows exactly how that would be interpreted in practice, but it may mean that China would try to ensure NK territorial integrity.
The second great unknown is that we don't know which political and ethnic assumptions NK act on because it is such a closed country. They may well believe they could win a war, and there is good evidence that they believe the right way to signal strength is through a willingness of escalations. That makes "tough" diplomatic response, especially when it is not thought out and haphazard like what Trump has been doing, dangerous.