1. Call DL to get rebooked. You will need to find space with award availability. Be flexible on routing and schedule.

2. Once you are booked, call China Southern and review the TIMATIC entry carefully with them. It's available free on the *A website among others. Do not rely or call on anything else as it's TIMATIC on which China Southern will rely. Once you are certain that you have it correct, ask China Southern to note your mother's record so that the problem doesn't reoccur.

3. In reading the TIMATIC entrey for a citizen of Taiwan, resident in the USA, traveling to Taiwan with a <24 hour connection in the PRC and on a Taiwan passport, the problem doesn't appear to be with a visa, but with the fact that the PRC doesn't recognize the passport so the TWOV rules don't apply.