How to get from Datong to Taishan and further to Pingyao (via Taiyuan ?)?

I am a little confused about your question. As for the Taishan, do you mean the Mt. Wutai in Shaanxi or Mt. Tai in Shandong Province? If it is Mt. Tai, it is unadvisable to travel from Datong to Taishan and then to Pingyao, since Datong and Pingyao are both in Shaanxi Province which is far from Taishan in Shandong Province. If it is Mt. Wutai, you can take the bus at Datong Bus Station to Wutai Mountain, which will cost you about 4 hours to get to the mountain from Datong.
After visiting the mountain, you can take the coach from Wutai Mountain Bus Station to Taiyuan. The coach leaves every 1 hour and will cost you about 4 hours.
Just as you said, you need to go to Pingyao via Taiyuan. You can take the bus from Jiannan Bus Station from Taiyuan, which will take you about 1.5 hours to get to Pingyao.
It is reasonable to visit the Pingyao briefly and take the evening train to Qingdao from Taiyuan.