Show a block only on the frontpage of the sub-domains
I recommend you to use context module for block displays with the domaincontext module extension.


  Domain Context module is an integration module for the Domain Access module and the Context module.
  
  The Domain Access module allows administrators to set specific
  settings for each of their domains that are using the same code base.
  The Context module allows you to assign blocks to regions (and more)
  given certain conditions that can be set in the Context admin.
  Currently when both modules are installed you have no interface that
  will allow you to trigger a context on a specific domain. This module
  adds a domain condition to the context administration so that you can
  trigger a context on a specific domain.