Howd Homeonttherange,

Your (typical) problem is that you are being too literal.  The term Personal Union is a very special, and limited Constitutional term.  It refers to two or more States (i.e., countries) that recognise the same Monarch as there Head of State, however their is no UNION OF THEIR PARLIAMENTS.  Some examples are,

(i).  The Union of Kalmar (1397).   Its members were the Kingdoms of Denmark, Norway, and Sweden.  This gave rise to the termUnited Scandinavia.  In 1562 (I believe) Sweden left the Union.  The resulting left-over Union of Denmark-Norway was dissolved in 1814, as being allied with Napolean "tunrned out badly".