Frequent unsharing/resharing of shared items is not a common use-case in Bitwarden.
If you want to approximate something close to what you were doing in LastPass, then I would suggest setting up one collection for each family member, plus one or more shared collections. For the member-specific collections, give the user Edit or Manage permission, and do not give permission to any other family members (other than the designated user); this should allow them to move items between their designated collection and the shared collections, and back.