Joomla caching with different modules for different sub domains

We want to setup cache for our Joomla 2.5 website www.aamcosocal.com. But we need some help. We have many sub domains for different store locations. We use redirects which points all the sub domain to the same page. For example, if you go to [login to view URL], you will see the same contents of www.aamcosocal.com. Each sub domain will have a different module to show the logo of that store. We use module assignments to show different module for each sub domain. (please look at attached image) The problem is when we use the cache function, it caches the same module for all sub domains. So even if I go to [login to view URL], I will see the logo from [login to view URL] If you are interested in this job, please let us know if you have done something like this before.