I am staying at the Brickyard Hotel on March 16. I will go to Mutianyu in the morning on the 17

John, it might be a really tight itinerary. The Wall is located in surburb area. You are suggested to get up early and charter a car for your round-trip to save time. Complete your hiking at noon and then get back to the downtown area to visit Tiananmen Square and Forbidden City one by one.
Get out from the northern gate of the Forbidden City before 6pm, walk eastwards for 20min to take airport shuttle bus line 13 from the Overseas Chinese Building. You will arrive at the airport in around one hour.