Yes, this can be done, but obviously you can’t test it with the free 2-person organization (although I am sure you know this already).
There are two ways to accomplish what you suggest:
Create a separate “admin” user who owns the family organization. Use this account only for administration. Then create a separate account for yourself as a personal account. This is the best approach, but only works if you have a small family and can afford to give up one license to the Admin account.
You can use your personal account as the organization owner, but you can restrict which collections you are able to view. In your case, you could set your permissions so that you will be able to view the Global and Selective1 collections, but not Selective2. See this post for more details:
The org. owner will be able to see items in collections (shared items) but only from the web vault, not from the mobile app or the browser extension. So to answer your question, true.
In practice it is not really a problem to me, because I rarely use the web vault.
9elsen: thanks for the confirmation. I was afraid this was the case. I can’t propose a password manager system to my family in which I can see all the login creds in the various Collections (like my daughter and son-in-law’s bank accounts). Bummer! I had high hopes for Bit Warden.
While this doesn’t directly solve the issue of the Org owner having access to all collections created in the Org. Your family members can be a member of multiple organizations, so if your daughter and son-in-law wish to only share items between themselves they could create a separate free two person Org to share their logins together apart from your family organization.
Kent: thank you for this clarification and strategy. I think this could work where they are members of their own 2-person family and members of my Premium Family org. This would also allow us to share (send) encrypted files within the Prem. Family org. (like tax documents, etc.).