I think that it's pretty clear at this point that, despite having diplomatic relations and trade with America for the last 50 years, Communist China is still a repressive dictatorship; if the plan was for trade and communication to result in their liberalization, it has utterly failed.
As a result, could the US President decide that Nixon was wrong to acknowledge the Chinese Communist Party as the legitimate government of China, and break off relations with them while formally acknowledging the Republic of China (Taiwan) as the legitimate Chinese government, in an attempt at forcing the CCP to renounce power and begin the process of holding democratic elections to determine the new government of China?
Can the US President issue an Executive Order declaring their ambassadors to the UN as Persona Non Grata (PNG), thereby forcing them off of the UN, since it's hosted in America, while encouraging the Republic of China to send ambassadors to replace them, banning all trade and travel to mainland China by US citizens, ships, or aircraft, or even deploying the US Navy to institute a blockade of mainland China to prevent any other nation from sending ships or aircraft there for trade (and shooting down or sinking any aircraft or ships that try to run the blockade)?
Would he need the support of Congress to do any of these things? I know that only Congress can declare wars, for instance.