It all comes down to enforcement. Without enforcement, laws and authority are meaningless.
Take the USA and England as analogous to Taiwan and China.
In the 1700s, England had a "One-England policy" and claimed authority over the US colonies. The US colonies disagreed. Some of the international community acknowledged the One-England policy. Some didn't.
At the end of the day England tried to enforce their authority/laws and lost. Thus, England actually didn't have authority over the US colonies.
I suspect something similar may happen someday with Taiwan (though hopefully with less violence than the American Revolutionary War).
cf. the Taiwanese government, the KMT, which at one point controlled the mainland, but was pushed into exile on Taiwan by the communists. The existence of a free Taiwan threatens the legitimacy of the communist government on the mainland: the PRC, like most propaganda-fueled authoritarian regimes, does not like anything that suggests there's an alternative to their system.
If George III had had as big a bee in his bonnet about reclaiming the colonies as the PRC has about Taiwan I doubt that America would have remained independent - compare the Uk Army of 1770's vs Wellingtons Army circa 1812.