China has a GDP of a little over 11 Trillion dollars while Taiwan's is 523 billion. China is over 20 times as large as Taiwan. It simply isn't large enough to leverage against China.
We see the same thing when we look at the most recent trade information from the Census Bureau:
Our balance of trade with China is 22x larger than that with Taiwan (top panel). Our exports to China are 5x larger than those with Taiwan.
Trying to use Taiwan against China is a fool's errand from the start.