Can my mother-in-law cancel my ID card and household registration book with my social security card?

You can cancel it. You can take your ID card and social security card to the local social security office to fill out the cancellation application. Generally, it can be cancelled the same day.

Social security card processing is as follows:

Those who meet the application conditions can make an appointment by telephone at the application outlets or apply for social security cards (including student ID cards) directly at the street (town) social security card application service outlets.

When applying, you need to bring your ID card, household registration book, application form (citizens with collective household registration need to bring the household registration certificate issued by the local police station or police station) and other related materials.