A trip to Longqingxia &. Mutianyu great wall

Hi;
I try to plan our family trip to china. Our last days of the trip will be in Beijing.
Except for the sites in Beijing we would like to visit Longqingxia &. Mutianyu great wall.
If understand from the map; there are something like 2.5 hours driving distance between those two places.
I thought that instead of going back to Beijing we should combine them with the same trip.
Option 1 - To get up early in the morning; & to take a driver that will take us to the both of places at the same day.
Option 2 - to take the public transportation; & then to stay at night in the area; & go to the other place at the second day.
Because our youngest son is 3 years old I dont want a trip with too many hours on the road; so Iam not sure what to choose.
I would be happy for advise what is the best way to do that trip