I think there's several ways to solve your problem, the easiest being:

use

Transform mychildtransform = gameobjectwithmytag.transform.FindChild(mychildname);

and then

mychildgameobject = mychildtransform.gameObject;

Of course there's many ways to get your gameobjectwithmytag object. The simplest being

GameObject.FindGameObjectWithTag

or GameObject.FindGameObjectsWithTag if there's many (of course you'll need to iterate through them and extract the one you're interested in).