Separating funds from an account

The easiest way to achieve what you want is to create a new Quicken Investment Account, perhaps named after the second mutual fund, then do a "Shares Transferred Between Accounts" action in the "old" Account into the "new" Account.  This will do a Remove of all the shares of the second mutual fund in the old Account and create Adds - one for each lot - in the new Account.  Each lot will have the correct "Date acquired" and basis.

This will leave the transactions associated with the second mutual fund in the old Account, which is fine since that's where they actually happened, and those transactions are easily isolated by running an Investment Transactions report if you want to look at the history of that fund.

Your questions about "'accounts' then 'hide and show accounts'" doesn't seem particularly relevant to your "headline" issue of "Separating funds from an account" as both the old and new Account should still be completely visible to your file, correctly.  To hide an active Account you right-click that Account in the Account Bar (list of all Accounts to the left or right of the screen) and select "Edit/Delete account."  That brings up the "Account Details" window where you click on the "Display Options" tab.