My mom is going to fly out from Vietnam to the US, and she has to layover 31 hours in Shanghai. I want her to exit the airport and stay at a hotel. Also, I have been doing the research about the 144 hours free transit visa. However, she doesn’t have a US Passport, and she just has a US Greencard and a Vietnamese Passport. I have been so worried if she's gonna have to stay in the airport for that long. Can anyone help me with this? Will she able to exit the airport?
Traveling on a Vietnamese passport, your mother does not qualify for either the 72-hour or 144-hour visa-free transit programs (unless it is a diplomatic or government service passport, or she also holds an APEC Business Travel Card). She will need a visa, and if she will be returning to Vietnam via China, she should get a visa for double (or multiple) entry to save time and money.
I would look into rescheduling her flights so that her total time between arrival in and departure from China is less than 24 hours, qualifying her for visa-free transit under the 24-hour program. She could then apply for an entry permit that would let her go into the city.
If that is not possible, a Type G (transit) visa is in order. She can obtain the application online, but it must be filed with the Chinese embassy in Hanoi in person, and if approved must also be picked up in person. Your mother does not need to do this herself; she can have a friend or relative do it, or hire an agent. Standard processing time for all visas is four days, and the fee is US$60 single or US$90 double, with surcharges for expedited processing, according to the embassy website as of July 2018.
The G visa would allow her to exit the airport and go into the city, so no need to be worried about being stuck in the airport for over a day.