Exclusive Relationship to organisation
I can answer for CiviRules: at the moment there is no such combination of condition and action available in CiviRules. 

But there is no stopping you to develop (or have someone develop) such a combination for you. It does not sound too complicated for someone familiar with CiviRules. 

Do you have the ability to develop this yourself? The condition would be 'relationship is of the type(s)' (that one already exists) and the action 'de-activate previous relationship' would have to be developed.

There is documentation on CiviRules here: https://docs.civicrm.org/civirules/en/latest/. 

Documentation on how to develop your own action is here: https://docs.civicrm.org/civirules/en/latest/create-your-own-action/