Beginner Help with Multiple Alignments

Don't think so.
Post your code here so the folks can see it. Use Insert/code from below.

TARTUP    =ALIGNMENT/START,RECALL:USE_PART_SETUP,LIST=YES
            ALIGNMENT/END
            MODE/MANUAL
            FORMAT/TEXT,OPTIONS, ,HEADINGS,SYMBOLS, ;NOM,TOL,MEAS,DEV,OUTTOL, , 
            TEMPCOMP/METHOD = AUTOMATIC,MATERIAL = Iron,CTE=11.3
              ,SET WARNING LIMIT = FALSE,MINIMUM = 10,MAXIMUM = 40
              ,PART SENSOR NUM=DEFAULT,X SCALE= 20,Y SCALE= 20,Z SCALE= 20,PART TEMP=20
            LOADPROBE/T3_8X200
            WORKPLANE/ZPLUS
            TIP/T1A0B0, SHANKIJK=0, 0, 1, ANGLE=90
PNT1       =FEAT/POINT,CARTESIAN
            THEO/<0,414,18>,<0,0,1>
            ACTL/<0,414,18>,<0,0,1>
            READPOINT/
A1         =ALIGNMENT/START,RECALL:STARTUP,LIST=YES
              ALIGNMENT/TRANS,XAXIS,PNT1
              ALIGNMENT/TRANS,YAXIS,PNT1
              ALIGNMENT/TRANS,ZAXIS,PNT1
              ALIGNMENT/TRANS,YAXIS,PNT1
              ALIGNMENT/TRANS_OFFSET,YAXIS,-414
              ALIGNMENT/TRANS,ZAXIS,PNT1
              ALIGNMENT/TRANS_OFFSET,ZAXIS,-18
            ALIGNMENT/END
CIR1       =FEAT/CONTACT/CIRCLE/DEFAULT,CARTESIAN,IN,LEAST_SQR
            THEO/<0,414,18>,<0,0,1>,24.5
            ACTL/<0,414,18>,<0,0,1>,24.5
            TARG/<0,414,18>,<0,0,1>
            START ANG=0,END ANG=360
            ANGLE VEC=<1,0,0>
            DIRECTION=CCW
            SHOW FEATURE PARAMETERS=NO
            SHOW CONTACT PARAMETERS=YES
              NUMHITS=4,DEPTH=7,PITCH=0
              SAMPLE METHOD=SAMPLE_HITS
              SAMPLE HITS=0,SPACER=-10
              AVOIDANCE MOVE=AFTER,DISTANCE=25
              FIND HOLE=DISABLED,ONERROR=NO,READ POS=NO
            SHOW HITS=YES
              HIT/BASIC,<12.25,414,11>,<-1,0,0>,<12.25,414,11>
              HIT/BASIC,<0,426.25,11>,<0,-1,0>,<0,426.25,11>
              HIT/BASIC,<-12.25,414,11>,<1,0,0>,<-12.25,414,11>
              HIT/BASIC,<0,401.75,11>,<0,1,0>,<0,401.75,11>
            ENDMEAS/
A2         =ALIGNMENT/START,RECALL:A1,LIST=YES
              ALIGNMENT/TRANS,XAXIS,CIR1
              ALIGNMENT/TRANS,YAXIS,CIR1
              ALIGNMENT/TRANS,YAXIS,CIR1
              ALIGNMENT/TRANS_OFFSET,YAXIS,-414
            ALIGNMENT/END
PNT2       =FEAT/CONTACT/VECTOR POINT/DEFAULT,CARTESIAN
            THEO/<25.304,412.973,18>,<0,0,1>
            ACTL/<25.304,412.973,18>,<0,0,1>
            TARG/<25.304,412.973,18>,<0,0,1>
            SNAP=NO
            SHOW FEATURE PARAMETERS=NO
            SHOW CONTACT PARAMETERS=YES
              AVOIDANCE MOVE=BOTH,DISTANCE=10
            SHOW HITS=YES
              HIT/BASIC,<25.304,412.973,18>,<0,0,1>,<25.304,412.973,18>
            ENDMEAS/
A3         =ALIGNMENT/START,RECALL:A2,LIST=YES
              ALIGNMENT/TRANS,ZAXIS,PNT2
              ALIGNMENT/TRANS,ZAXIS,PNT2
              ALIGNMENT/TRANS_OFFSET,ZAXIS,-18
            ALIGNMENT/END

It is hard to work on something without CAD as I did 2 years ago.  as ArkansasBeeper said, post you code so others could help you.

Its hard for me to post my code because my CMM has to run independent of our network due to some overly complex security protocols here. But, based on the response, I can "leap frog" a new alignment (A3) based on geometry I have created within the previous alignment (A2)? As long as that is a true statement, I will spend the time to find my mistake. I probably selected the wrong feature when defining my A3. Thanks for the confirmation.

I would not leapfrog on a CMM if the part fits within the volume of the machine. 
It sounds like there is an error in your alignments or a bad hit somewhere. 
Try doing it again, 3 hits for a plane, 4 hits for each circle, create a line between the circles. Do your first alignment as...
Level plane to Z
Set Z origin to plane
Set XY origin to one of the circles
Rotate X or Y to the line (whichever is appropriate for your setup)

Once that is done, assuming your using a Hexagon machine with a NextJogBox, hit the button to change to "part" coordinates and slowly move the probe around and see if its following your parts direction. If you move between the dowel holes your machine should move in a straight line in whichever axis your rotated to.

As ArkansasBeeper  said it looks like standard 3-2-1 Alignment scenario. perform a progressive alignment (Level, Rotate & origin step by step in each alignment) by which you are able to notice where you are going wrong. The number of alignments may increase but believe me it's clear and easy to understand. Make sure your theoretical inputs are correct for XYZ & IJK.

 Shivarajkumar BARAGI  I agree with you 100%,

I also create each subsequent alignment on STARTUP, it helps me not to repeat the error or if sometimes I have to go back and change something in the alignment, because e.g. Revision has changed and corrections need to be made or if something went wrong.