The alliance between Seoul and Washington has existed since the division of the peninsula at the end of WWII. This alliance grew stronger in the aftermath of the Korean War when US forces made up the bulk of a UN coalition to fight against the Korean People's Army and Chinese military forces. This military alliance remains today in the form of a strong US presence in South Korea along with intelligence cooperation in an effort to for-see any significant provocations from Pyongyang. The US nuclear umbrella is one of the most important factors in the region with Japan and South Korea both relying on assurances from Washington that they will use the threat of US nuclear force for their national security. This is one of the main reasons Pyongyang sought to develop nuclear weapons in the first place since they felt they didn't hold a powerful enough hand in negotiations with the US, which is still formally an enemy nation.
With that in mind it becomes clear how it could benefit the DPRK if Washington and Seoul were to split on their long-term goals; something which both countries have denied is happening. Recent reporting suggests that Marshall Kim Jong Un instructed his military forces to remain in-place and not to take any unplanned provocative action which could negatively influence the Hanoi summit. This course of action demonstrated how keen the government was to secure an agreement on sanctions relief. This was undermined when the US side apparently suggested a Libya-style strategy which involved shipping all Pyongyang's nuclear material to America. This was received very badly and may have been the catalyst for the failure of the talks. However, despite a few diplomatic issues between Pyongyang and Seoul, the relationship between the two Korean nation-states has been relatively relaxed. If Kim Jong Un were to continue to push for more joint-economic projects such as reopening the Kaesong industrial park and accelerating railway-cooperation projects then it may sway the Seoul government away from the idea of immediate denuclearisation and begin to push the two cross-Pacific allies apart.
Washington is focussed on denuclearisation since that is the only issue which directly affects it. The thought of the DPRK possessing an ICBM with the ability to strike the mainland United States shocked the world in 2017 and led to the diplomatic engagement which flourished in 2018 and may have just fallen apart in Hanoi. Seoul however will need to live next-door to the DPRK whether or not denuclearisation occurs. This provides a strong incentive for Moon Jae-in to participate in projects aimed at improving relations rather than forcing Pyongyang's denuclearisation. At the moment he is walking a fine line but as the US-DPRK negotiations begin to lose steam and break-down, which is now more likely than ever, the government in the south may be forced to choose a side. Abandon joint-projects and side with the US to demand denuclearisation, a move which would please South Korean conservative groups, or split with the US to work more closely with their nuclear neighbour in the hope that a strong relationship will serve as a better deterrent than the US nuclear umbrella.