Hello,
302 is NOT an error - simply a pointer to a different URI for the resource. As you have not provided an example URI you are accessing or communication trace / log, it is impossible to say wether the 302 is correct and you need to change your call, or if there really is a potential problem (i.e. redirect to login form) that needs to be addressed in a different manner.
What I'd expect from your setup is that you are being redirected to the CAS login form as Alfresco does not yet know the user currently logged in the third party client. This is correct behaviour since having a CAS which serves both of the applications does not automagically mean you can perform AJAX calls between these applications and have your user transparently authenticated. Depending on how the CAS session token is managed and your AJAX call constructed, you may need to adapt either Alfresco or your client to ensure the CAS session token is properly passed and evaluated in the AJAX exchange.
Regards
Axel