Well, Longmen Grottoes is close to Luoyang and Shaolin Temple is close to Zhengzhou. And, both of these two cities could be reached from Xi'an easily by train. However, if you going to Beijing then, it seems that Zhengzhou has much easier transportation, both by train and by air. So, I think you could first arrive in Luoyang from Xi'an and then take a train to Zhengzhou in 2 hours. After visiting the Shaolin Temple, you could leave for Beijing from Zhengzhou.

With all respect to Mr Shan,I think the best choice is to go to Luoyang from Xi'an by train.After visiting the Longmen grottoes and other scenes,you can go to Shaolin temple directly,maybe less than 3 hours by big and soft bus from Luoyang to Shaolin temple.After that you can leave for Beijing from Zhengzhou by train or by plane.You can also first go to Zhengzhou from Shaolin temple,then leave for Beijing.