Entry and exit in Shanghai different airport

Trisha, there are no problems because using different airports is perfectly allowed, but your total transit time based on your scheduled arrival/departure is not allowed to be longer than 24 hours! If your total transit time is shorter than 24 hours, you will be covered by 24 hour visa free transit and you do not need any kind of visa.

The first thing you will do upon your landing in Shanghai (regardless which airport) is to approach 24/144 hour visa free transit counter where you will apply for a temporary entry permit by presenting your flight tickets and your hotel booking if your layover is during the night. This application is free of charge and I encourage you to print out the tickets and your hotel booking. After that you will head to the immigration and then to the city to spend your time on your own before taking your next flight. The same thing you will repeat on your second arrival in Shanghai. Have a nice journey both ways.