I think the situation is a lot more complex than even the BBC can relate. Certainly Trump's chief advisor on China, Peter Navarro is no expert on either China or the DPRK (see here:
http://foreignpolicy.com/2017/03/13/peter-navarro-profile-national-trade-council-donald-trump-china-expert/ )
I go to China three or four times per year and talk a lot to the people there - both Chinese and Chna-friendly westerners.
China wants to avoid two things: war (or nuclear strike) on its own territory and refugees coming from DPRK into Liaoning and other nearby Provinces.
China also wants the US to remove the THAAD (Terminal High Altitude Air defence) missile system from south Korea. That has a radar that can see around 2000km. Beijing is 1000 km from Seoul; Hong Kong is 2000km from Seoul. That radar can see deep into Chinese territory. The Chinese see THAAD as an aggressive act by the USA.
We know there have been discussinos between US and China over THAAD in which China has promised to stop DPRK's weapons development programmes if the US removes THAAD.
The US has turned down that offer.
Ask yourself, how did DPRK develop nuclear fusion bombs (H-bombs) and ultra-long range ballistic missiles in the space of a couple of years. It is simply not possible without external help. That means either Russia or China.
I am convinced China has been helping DPRK with these systems in order to introduce uncertainty into the foreign relations environment to convince the USA to remove the THAAD system from S Korea.
Trouble is, Trump is calling their bluff. I guess the Trump supporters see that as courageous; others see it as foolhardy.
The key is persuading China that it is in their own interests to stop supporting DPRK. You do not do that by making conditions in DPRK even more deprived. You do it by treating China with some respect.
IMHO.