Unity: Detect Child Trigger inside Parent Script

What you talk about is called self-collision. One way of handling this is to ignore certain colliders, take a look at the documentation here.

If I understood you correctly you have an GameObject hierarchy like so:

parentGO (contains player mesh and Capsule Collider 2D)
|-childGO (contains attack mesh and Mesh Collider 2D)

I'd attach to the childGO a script, which should register collisions on its polygon collider and notify the weapon script on the parentGO of the object being hit. The weapon can then deal the damage to the target.

I know most likely You got your response, but It is also good to mention, that maybe You should think about separating these object and attaching them to new GameObject, that have a script holding both colliders - that might be more reliable and easy to read.

You can use Collider2D.IsTouching(Collider2D other);

Here is documentation for IsTouching

Or write custom script that uses the observer and notify the main GameObject that the collision occurred.

private Action _onGameObjectCollided;
private void OnTriggerEnter2D(Collider2D col){
    if(col.gameObject.CompareTag("TAG")
        _onGameObjectCollided?.Invoke();
}
public void AddOnColliderEnterObserver(Action observer)
{
    _onGameObjectCollided += observer;
}

public void RemoveOnColliderEnterObserver(Action observer)
{
    _onGameObjectCollided -= observer;
}

And inside new GameObject:

collider.AddOnColliderEnterObserver(MethodToCallOnTriggerEntered);