Taxi fare for 4 adults from capital airport to Raddison Blu Hotel in Chaoyang.

From the airport to hotel, the cab fare is CNY 60 to 70 per car in the day time. Usually, a taxi can allow four passengers. But if you have too much luggage, you may need two.
From the hotel to Badaling Great Wall, it costs around CNY 300 for the single trip; it may be higher to Mutianyu. But I'm afraid regular taxi wouldn't like to go that far. In the case, you can hire a car. As I know, this website provides car rental service. They have warm-hearted drivers. If interested, their contact information is traveltravelchinaguide.com.