The monk who ignored his visiting wife and infant son
Upekkha is freedom from all points of self-reference; it is indifference only to the demands of the ego-self with its craving for
  pleasure and position, not to the well-being of one's fellow human
  beings. True equanimity is the pinnacle of the four social attitudes
  that the Buddhist texts call the "divine abodes": boundless
  loving-kindness, compassion, altruistic joy, and equanimity. The last
  does not override and negate the preceding three, but perfects and
  consummates them.


BB's explanation here sounds exaggerated &amp; too lofty. Metta is arguably the pinnacle of the social attitudes and equanimity governs the other social attitudes. A lingusistic root of 'upekha' is 'to look'. It means 'to observe others, looking to help others, but always knowing others are the heirs to their actions'. That is, equanimity understands you can only help others when they are willing to help themselves.  


  Did he lack compassion?


He did not lack compassion. Compassion is non-cruelty &amp; wishing to help others overcome suffering. The ex-wife was not seeking to end suffering but craving to get her former husband back. If the wife walked away from the child &amp; never returned to the child, the monk abandoning the child would have been cruelty. But this did not occur. The monk obviously had compassion but governed his compassion with equanimity, testing the kamma or motivation of his former wife. The former wife returned to look after her child, therefore the wife followed her personal path, which was motherhood. 


  Should he not have addressed his former wife compassionately, and
  given her an explanation of the Dhamma, and the path to the end of
  suffering?


Absolutely not because the Dhamma says Dhamma is only taught to those who ask for it (AN 9.5). 

This story is an excellent example of the practice of equanimity, namely, observantly looking on to help another person according to the kamma or personal disposition of the other person. The wife demonstrated motherhood was her want &amp; destiny. If (hypothetically) the wife completely abandoned the child &amp; there was no one else to look after the child, the monk would have looked after the child himself, similar to how Rahula was ordained as a novice at 7 years of age.