Always stay upright and follow parent's y and z rotation

[Irish-Merlin]

How do I force a child object to always stay upright and follow the parent’s y and z rotation?

I’ve created an object that resembles to this:

I’m using rigidbody on the parent with two child objects containing wheel collider in each. I was able to move it and turn. All okay, but I just wanted the main body to stay up-right. When moving and hitting rocks on ground, I need the whole object to freely rotate in any direction as it is driven by physics. When the object is flipped upside down, the main body is to rotate back to its upright position.
I added this to the parent:

void Update()
{
    transform.Rotate(new Vector3(0.5f, 0, 0));
}

I added this on a child:

void Update()
{
    transform.LookAt(Vector3.up);
}

But that causes the child to always face up and cannot rotate in x and z axis when the parent rotates in all axis.

To ensure the child follows the parent’s y and z axis, I tried this:

void Update()
{
    transform.LookAt(Vector3.up);
    transform.localEulerAngles = new Vector3(transform.localEulerAngles.x, 0, 0);
}

When you start the game, the child rotates, but wait until the parent finishes its revolution, then the child will remain facing upright. Another full revolution of parent, the child then rotates.

I’ve included an [45667-spintest.zip|45667] to demonstrate what I’m trying to do.

How do I force a child object to always stay upright and follow the parent’s y and z rotation?

EDIT:
After reading Eno Khaon’s answer, I realize that the attached demo I provided was not clear. I’ve updated the file to explain the demo better.

[45698-twowheelsobject.zip|45698].

[Cow-Necromancer]

under the rigid body, lock the rotation

[Eno-Khaon]

Maybe I’m looking at this the wrong way, but it sounds like you should try applying torque.

Using AddTorque on the parent should give you a means of flipping back upright if flipped over, then you can scale the strength of the torque applied relative to the dot product of its transform.up and the global Vector3.up values.