Any Corpus Christi resident may register for and receive a free library card by completing a library card application and presenting identification that includes a local residential address and photo. here (pdf document).
Yes, your children can get a library card with the parent or guardian present with ID and documentation for the child (such as birth certificate, report card, social security, etc).
If your card is expired, simply call or go to any branch for a free renewal.
Report the lost or stolen card to any branch and you will be issued a new card with a different number. A small replacement fee of $2 will apply.