Datong Grottos and Hanging Monastary

Yes, it is possible to visit both of these in one day with a private guide.
It may be hard to find an English guide when you arrive, I suggest you to book a tour in advance. Then they will pick up you at local railway station to start your journey.
I once joined a tour of TravelChinaGuide to visit Mt. Wutai in Shanxi, which left me deep impression. I think they can arrange a private tour for you according to your requirements. You may try to contact them at travelchinaguide.com|tours.
Hope you have a nice trip there.