I recently has an issue with a rocket going through targets due to speed and even with continuous dynamic collision detection I couldn't keep this from happening a lot.
I solved this using a script "DontGoThroughThings" posted in wiki.unity3d.com. This uses raycasting between current and previous positions and then ensures the frame ends with the colliders connected for messages an OnTrigger event. Has worked everytime since and it's just a matter of attaching the script so super easy to use.
I think the physics answer is as others have suggested to use multiple components with different drag although typically I think you only want a single RigidBody on the parent. Instead of direction using transform.LookAt you could try and calculate using Quaternion.LookRotation from the rigidbody.velocity. Then use Vector3.Angle to find out how much are are off. The greater the angle diference the more force should be experienced and then use RigidBody.ApplyTorque. Maybe use the Sin(angleDifference) * a constant so less force is applied to torque as you approach proper rotation.
Here is some code I used on my rocket although you'll have to substitute some things as I was pointing toward a fixed target and you'll want to use your velocity.
var rotationDirection = Quaternion.LookRotation(lockedTarget.transform.position - this.transform.position);
var anglesToGo = Vector3.Angle(this.transform.rotation.eulerAngles, rotationDirection.eulerAngles);
if (anglesToGo > RotationVelocity)
{
var rotationDirectionToMake = (rotationDirection * Quaternion.Inverse(this.transform.rotation)).eulerAngles.normalized * RotationVelocity;
transform.Rotate(rotationDirectionToMake);
}