Can Taiwanese passport holder with no Taiwanese ID card enter Xiamen by Ferry from Kinmen, Taiwan

My sister is holdng a US passport and she could only get a one-entry China visa. The China Embassy said they don't issue double-entry tourist visa now. She is the only one in our group who is holding a US passport and it's our first time travelling together as a family and first time going to Kinmen, Taiwan via Xiamen. We have booked tickets to fly into Xiamen and realised that my sister can take ferry into Kinmen but she would not be able to return to Xiamen as she is holding only a one-entry China visa.

Can someone advise if she is able to get a China visa on arrival on her return journey from Kinmen to Xiamen? She also hold's a Taiwan passport but no Taiwanese ID card. Can she use her Taiwanese passport without Taiwanese ID card to enter Xiamen from Kinmen
It's crucial that we all go to Kinmen as my dad was born in Kinmen and he passed away last year. So we decided to bring our mom to Kinmen this time to visit dad's birthplace as we all haven't been there.

Would appreciate if someone could give us an advice.