Start your "child" activity with just startActivity, then when back pressed on the child activity, capture onBackPressed on the child activity and start your parent activity again with a new intent like so:
@Override
public void onBackPressed() {
startActivity(new Intent(this, FirstActivity.class)
.setFlags(Intent.FLAG_ACTIVITY_CLEAR_TOP | Intent.FLAG_ACTIVITY_NEW_TASK));
}
This should start you fresh with a newly started parent activity.