Hi ColumbusDad,
Thanks for contacting Apple Support Communities!
We understand that you'd like to block callers from using SharePlay with your children.
Although you won't have the option to block SharePlay on your kids contact's devices, you could block the contact from contacting your children as outlined here: Block phone numbers, contacts, and emails on your iPhone or iPad - Apple Support
"Block a phone number, contact, or email
There are a few ways that you can block phone numbers, contacts, and emails.
Phone
From the Phone app, tap Recents, then tap the Info button
next to the phone number or contact that you want to block. Scroll down, then tap Block this Caller.
FaceTime
From the FaceTime app, tap the Info button
next to the phone number, contact, or email address that you want to block. Scroll down, then tap Block this Caller.

Messages
From the Messages app, open the conversation, tap the contact at the top of the conversation. Tap the info
button, scroll down, then tap Block this Caller.
Mail
From the Mail app, open the email that has the contact that you want to block, then tap the contact at the top. Tap Block this Contact."
We hope this helps you.
Take care!