WolfishMusings,
If the infant is a definitive Amaleki, his parent must be one too. Therefore, when making the “hareini” I would have in zin to be yotzei on the parent as well.
Like any mitzvah I would be overjoyed in having the zchus to be mekayim it. How often in our generation does one get the zchus of killing an Amaleki? (Of course doing this would necessarily be conditioned upon the certainty of not facing secular civil consequences for being mekayim this great mitzvah. This isn’t a mitzvah one is required to be msiras nefesh for.)