What kind of Visa is required if we are entering China twice

I have a US passport and I am flying to Shanghai arriving 4/2/16 at 7:10 PM to visit my daughter's home (a teacher at an international school). We are flying to Thailand on 4/4 at 10:15 PM and then returning to Shanghai on the 9th at 8:50 AM. Due to our airline changing our schedule, we are now returning to the US on the 10th at 11:40 AM.
Is it possible to go with a visitors 72 or 144 hour visitors fre transit or since we are traveling to Thailand do we need to obtain an actual entry permit?