Taiwan is just one of Danny's many suitors, and they are one pair in the lover's hexagon of the South China Sea (China, Vietnam, Malaysia, and Philippines like him too). And with two of Danny's children
hostage under her adoptive care, he has to follow her bidding and declare his recognition of her legitimacy as the only Chinese government or else she would leave him at Yao's mercy ( and he's not very merciful).
Danny's relationship with Taiwan comes mostly from the current disputed status of the Spratly Islands between China, Taiwan, Vietnam, Malaysia, and the Philippines. (
Poor Danny, having to service five nations at the same time. I don't envy him).