You have complete control over what your family member on the app can and cannot see.
Transactions: To edit whether your family member can see a specific transaction, select the avatars next to any transaction. As long as you are the one who added the account, you'll see the ability to mark that transaction as Private. Doing so will prevent the software from displaying that transaction to anyone but you.
Accounts: Changing the shared status of an account is easy! Just head to the More tab. Select Linked Accounts and select the account you want to update. Then select the Sharing row and choose the setting. Just remember to hit save and you're all set.