How to block access to app store

How can you entirely block access to the app store? Even after removing access from the home screen, you can still access it from the text messaging screen. My goal is to prevent my family from having access to adult content (and comparable - eg. lingerie) which may be indirectly accessed (bypass search restrictions) by "hoping" through the "you might also like" feature on the app store.

In short, many of these "clothing" apps are listed as 4+. I want to block access to the app store entirely.