New MacBook Air

1. Family Sharing does not in any way share any info. It shares apps and purchases, and iCloud storage, and apple subscriptions, but it does not share info like messages, emails, photos (except explicitly shared ones) etc...
2. If you are sharing info, you are using Family Sharing wrong. Each person in Family Sharing should be using their own Apple ID. If every body is using your Apple ID, then you are defeating family sharing entirely.
3. Make sure each person has their own Apple ID, and said Apple IDs have been invited to Family Sharing.

There should be no info sharing this way.

There isn't a way to use a different Apple ID and still be under the family account.

You can have someone set up Family Sharing between the IDs if you want to be able to share purchases made with the IDs.

Family Sharing.         

Family Sharing - Set up.