You can achieve this in multiple ways, but I'll give you one supposing that both Fragments are displayed at the same time.
In your ChildTwo use getParentFragment to get MainFragment.
MainFragment parent = (MainFragment) getParentFragment();
String edit_text_value = parent.getChildOneText();
In your MainFragment you need a reference object to your ChildOne fragment.
public String getChildOneText()
{
return mFirstFragment.getEditTextValue();
}
Finally in your ChildOne fragment create a method to return your EditText.
public String getEditTextValue()
{
return my_edit.getText().toString();
}
Hope it helps!