Here is a combination of the above answer's that solved my specific situation:
Centering two separate labels within a layout that also includes a button in the left most position of the same layout (button, label, label, from left to right, where the labels are centered relative to the layout containing all three views - that is, the button doesn't push the labels off center).
I solved this by nesting two RelativeLayout's, where the outer most layout included the
Button and an Inner-RelativeLayout.
The Inner-RelativeLayout contained the two text labels (TextView's).
Here is a snippet that provides the details of how the centering and other layout stuff was done:
see: RelativeLayout Gravity not applied? and
     Gravity and layout_gravity on Android
for the difference's between gravity and layout_gravity.
Tweak the paddingLeft on the btn_button1 Button to see that the TextView's do not move.
(My apologies to havexz for the downvotes. I was too hasty in thinking that just b/c your suggestions didn't solve the exact question being ask, that they do help to solve very similar situations (the answer here solves a very specific situation, and only the combination of all these answer's solved my problem.  I tried upvoting, but it won't let me unless I edit the answer's, which I don't want to do.)
<RelativeLayout
  xmlns:android="http://schemas.android.com/apk/res/android"
  android:id="@+id/rl_outer"
  android:layout_width="fill_parent"
  android:layout_height="50dip"
  android:background="#FF0000FF">
  <Button
    xmlns:android="http://schemas.android.com/apk/res/android"
    android:id="@+id/btn_button1"
    android:layout_width="wrap_content"
    android:layout_height="fill_parent"
    android:background="#FF00FF00"
    android:text="<"
    android:textSize="20sp"
    android:paddingLeft="40dip"/>
  <RelativeLayout
    xmlns:android="http://schemas.android.com/apk/res/android"
    android:id="@+id/rl_inner"
    android:layout_width="wrap_content"
    android:layout_height="fill_parent"
    android:background="#FFFF00FF"        
    android:layout_centerInParent="true"
    android:gravity="center">      
    <TextView
      xmlns:android="http://schemas.android.com/apk/res/android"
      android:id="@+id/tv_text1"
      android:layout_width="wrap_content"
      android:layout_height="fill_parent"
      android:background="#FF505050"
      android:textSize="20sp"
      android:textColor="#FFFFFFFF"
      android:text="Complaint #"
      android:gravity="center"/>     
    <TextView
      xmlns:android="http://schemas.android.com/apk/res/android"
      android:id="@+id/tv_text2"
      android:layout_width="wrap_content"
      android:layout_height="fill_parent"
      android:background="#FF505050"
      android:textSize="20sp"
      android:textColor="#FFFFFFFF"
      android:layout_toRightOf="@id/tv_text1"
      android:gravity="center"/>
  </RelativeLayout>
</RelativeLayout>