It is not possible to disable the Play Sound function.
However, it is only possible to do this from devices that are signed in to your Apple ID. So you can ensure that your family does not have access to iPhone, iPad and Macs that are signed in with your Apple ID. You can also change the passcode for those devices so they don't have access.
Alternatively, you can set up Guided Access, on iPhone and iPad. With Guided Access, you can prevent your family from using apps other than the one they have open. For example, if they are playing a game, then with Guided Access you can prevent this game from being left.
You will find Guided Access here:
Settings → Accessibility → Guided Access
You can find more information about Guided Access here:
Use Guided Access with iPhone, iPad, and iPod touch - Apple Support