Hello,Ms.Ririen
You cannot go to Badaling Great Wall by subway directly. You can use subway as a part of the tranpoort mode of your trip. As red wall hotel is next to Tiananmen East Subway station, you can ride on subway to Deshengmen and then take bus no.919 which runs directly from Deshengmen to Badaling. Remeber that general bus cost 7RMB per head while air-conditioned bus cost 12RMB per head. The frequency is 5 minutes. It is the cheapest and best transport.