we are coming into xian north train station and going to embassador international hotel

I suggest you take the subway line 2 from the train station and get off at Xiaozhai Station. Then take a taxi to your hotel, about 5km.

You don’t need to book the private pick up service, it’s too expensive.

When you get out of the train station, you can easily find a taxi to your hotel. It may cost CNY 100.