The bullet train is available at Beijing North Train Station (Xizhimen Train Station). You can take subway to Xizhimen and then walk to the train station nearby. The cost is 19 or 23RMB for second and first class seat. You can go to Summer Palace after Badaling. The first train to Badaling is 8am. Then you can finish the trip at noon. Take 13:57 (train no. Y578) back to Beijing North. Then take subway Line 4 at Xizhimen to Beigongmen Station. That is the north gate to Summer Palace. Then you can have a short time there. You can shorten your time in Badaling.