Do you mean that you've had, for example two meme parents (Memepapatchi and Mememamatchi)? That doesn't nesessarily mean that you have pure family (pure families have only two eggs, so if you had more, they're not pure families).
Here's how you get a pure family:
Mame family: To get Mamatchi, train your boy child with smart items until he reaches 80-100% bonding. Then get 100% bonding and marry him with Chantotchi.
Meme family: To get Memetchi, train your girl child with cheerful items until she reaches 80-100% bonding. Then get 100% bonding and marry her with Mumutchi.
Kuchipa family: To get Kuchipatchi, train your boy child with easy-going items until he reaches 80-100% bonding. Then get 100% bonding and marry him with Yonepatchi.
Violet family: To get Violetchi/Furawatchi train you girl child with smart items until she reaches 40-70% bonding. Then get 100% bonding and marry her with Sukatchi.
But if you're 100% sure that you had pure family, did you know that the pet only appears in sertain animations. You can also see it when you check your family type (pet is in lower right corner).