IF you really want to use 'Unified' folders for all your mail accounts, but not that other persons account:
Right click on the 'Unified folder eg: Unified Inbox' and select 'Properties'
Click on 'Choose'
Uncheck the Inbox for the other persons account.
Do the same for all the other 'Unified folders'.
This means the 'other person' account will now contain everything and be displayed below. You can collapse the other persons mail account name folder and only expand it when they need to see all their emails.
Alternative is use separate Profiles:
Have two profiles - one which has all your mail accounts and the other for the member of family.
That means neither of you can see the other - it also means when you start Thunderbird you need to invoke the Profile Manager, so you can choose the profile you want.
If you have a shortcut icon on Desktop - right click on it and select Properties
On 'Shortcut' tab - Where it says 'Target', you may see something like this: