Unable to configure multiple Exchange accounts in Outlook 2013

Question

This is a complicated issue so I will try to describe it the best I can.
I have a client with two SBS servers for two different organizations in two different locations.  Each server handles completely different domains.  Let's call them A and B.
The issue is this...using Outlook 2010 or 2013 on clients at location B, I can configure Outlook for the users mailbox on server B just fine.  Some of the users at location B also have mailboxes on server A.  When I add a 2nd Exchange account for
the users mailbox on server A, things get weird.  
Sometimes, when I start Outlook after adding the 2nd Exchange account, Outlook will show only one mailbox, but it is incorrect.  The top level will show it is a mailbox on server B, but it contains email from server A.  When this happens, email
actually transfers from one mailbox to the other.  I have to close Outlook quickly before things get out of hand. About a year ago, I determined that if the user has the same username and password for their mailbox on server A and server B, this would
cause the problem.  So I changed the users' username on server B and it seemed to work with Outlook 2010.
Now, a year later, we have a new user with Outlook 2013 with a mailbox on server A and server B, who works in location B.  I setup Outlook 2013 with mailbox B and it's fine.  I add a 2nd Exchange account for mailbox A to their Outlook Profile,
and when I launch Outlook, it shows both.  BUT, the mailbox A has nothing in it, and the status shows "This folder has not yet updated.  CONNECTED".  Mailbox B shows "All folders up to date.  Connected to Microsoft Exchange".
 Also, existing email from mailbox A starts showing up in mailbox B.  If I go into mail account settings, I get the "Outlook is using temporary mailbox" dialog, meaning something has moved.  If I look at the two accounts, both look
to be using the same OST file, even though under data files, there are two OST files, one for each mailbox account.  If I delete the 2nd Exchange account (A), Outlook works again for the single mailbox on server B.
I've tried configuring the accounts without cached mode, but that doesn't work either.  Mailbox B had a delegate account (Full access permissions) to another account on server B, but I have tried removing that also, but no change.
I cannot figure out why I cannot have two Exchange accounts, one from each server (A and B) in Outlook 2013/2010 at the same time.
HELP!  
Thank for any ideas.  I hope I haven't made this too confusing.  One last thing...when I add the 2nd Exchange mailbox, I authenticate with the username on server A with domain\username and their password.  The authentication seems to be accepted
fine and without error.  I have also tried configuring the 2nd account using "automatic" instead of configuring manually.  Same problem.

Answer 1

OK, I have done some more testing as you suggested.  I created yet another new profile with just mailbox A.  When I start Outlook, I see the users mailbox, plus a mailbox that the user has been given Full Permissions to (a delegate?).  There
is one more mailbox that this user has full permissions to, but it did not auto-add itself, so I added the mailbox through the account properties.  Now, all three mailboxes at location A are in Outlook (users mailbox and 2 delegate mailboxes).  In
Outlook, on the left, has at the top the users main mailbox, and then below it are two other "branches" for the delegate mailboxes.  I did NOT use cached exchange mode, btw.
I quit Outlook and edited the profile, adding another exchange account for the users mailbox at location B.  I did a "check-name" and authenticated OK.  
I launched Outlook, and the same (wrong) thing happens.  On the left pane of Outlook, at the top, it shows it is the users mailbox at location B (the main branch says Mailbox name -- location B), but all the folders and content are from mailbox at location
A.  Outlook has mixed it up, and it is at this point that email starts moving between mailboxes, so I quit Outlook quickly.  It did show the two delegate mailboxes from location A, but there were just three "branches", and nowhere is there
the real mailbox B.
Can it have anything to do with the fact that these accounts have delegates (or are given full manage permissions to other mailboxes on the  server)??
UPDATE:  I just determined something.  When looking at the Outlook email accounts dialog, for each account it shows the default delivery location.  For the first account (location A), it shows:
"Selected account delivers new messages to the following location:  usersemail@locationA\Inbox".
When I add the users mailbox for location B, it shows:
"Selected account delivers new messages to the following location:  usersemail@locationB\Inbox".
However, when I start Outlook, and see that things are wrong and quit, I go back into the accounts dialog, and BOTH accounts are set to deliver to the SAME location:
"Selected account delivers new messages to the following location:  usersemail@locationA\Inbox".
So now, the 2nd exchange account has changed it's location to deliver to mailbox A instead of B.
Crazy stuff.