Is there any direct public transport from Beijing T2 to either Datong or Chengde

I'm afraid no direct public transportation is available upon your landing. Then you'd better stay overnight at the airport, where there are hourly lounges for your choice. In the next morning, you can take airport shuttle bus line 3 to BJ Railway Station to take a train to Datong or Chengde, for which you are advised to book the train tickets in advance. By bus, you can take shuttle bus line 7 to BJ West Train Station, where transfer to subway line 9 to Liuliqiao and then walk to Liuliqiao Long-distance Bus Station to catch a direct bus to either of the two destinations.