transfer Shanghai Hongqiao to Pudong airports at night

Hi, I have a domestic flight arriving Hongqiao airport at 22:00. I then have an international flight departing Pudong airport at 10:20 the following day. I will be travelling with a family of 4 persons. I'm thinking to immediately transfering to Pudong airport, then shuttle to the Shanghai Airlines Travel Airport (closest hotel I can find to Pudong airport). Will the Hongqiao Pudong shuttle still be running that late at night? How long will it take? Is it worth considering taxi direct from Hongqiao to the hotel? How much would it cost? Do you have any other suggestions to make this transfer as easy as possible? Thanks!