The third law states that you can't exert a force without the same magnitude of force being exerted back. That's just what forces are - they are interactions.
The second law (and the 1st law which is just a word version of the 2nd) looks at one body (not two) and determines how it moves given all the forces acting on it.
Sled has F of father's pull sideways. Up and down weight and normal force cancel (Child is just part of sled)
Father has same force pulling in the opposite direction as he pulls on the sled, but he also has traction from the friction responding to his pushing backwards on the ground (The ground's reaction force pushes him forward - If there is no friction with the ground, the father can't exert any force and can't move the sled)
The action/reaction pair of forces do not cancel because they are exerted on different bodies.