Perhaps your wife has a limited vocabulary:
“...a pet in Spanish can be referred to as una mascota (the same word is used for a mascot, such as an animal symbolizing a team), un animal doméstico (the adjective doméstico can also be used to mean “pet” as an adjective, as in un perro doméstico, a pet dog) or un animal de compañía (again, the phrase de compañía can be appended to an animal’s name to indicate it is a pet).”
http://spanish.about.com/od/spanishvocabulary/a/pets.htm
They are domestic animals, like cows or goats (and don’t live in the house); nowadays, Spain is even weirder than the US, so maybe the language has evolved to reflect that: they probably use a new word for “pet”, and dropped “son” and “daughter” from the dictionary.