It's China imposing the effective ban. For PRC citizens to fly TO Taiwan, the PRC government needs to issue a permit (the 大通证 you mention above). Right now they're not issuing them for tourism purposes.

For PRC citizens to ENTER Taiwan, they need a document issued by the Taiwanese government, the 入台证. If your mother is transiting and NOT ENTERING Taiwan, this is irrelevant.

Three exceptions are Chongqing, Nanchang, and Kunming. From these 3 airports, PRC citizens are allowed (by the PRC government) to transit through Taiwan onto a third country, provided the passenger has the ticket and valid visa for the destination country. Currently there is only a direct flight to TPE from Chongqing.

Caveat: I haven't done this nor do I have any first-hand knowledge. This is the best info based on what I've read.

Note: if you need to change airports during transit then you'll need a 入台证 since you're entering Taiwan.