Looks like you need to organize the view and models for your modules underneath the module directory.
Take a look at the docs:
Zend Framework: Documentation
In your case it would look something like this:
Code:
..../application/admin/controllers/*
..../application/admin/models/*
..../application/admin/views/*
And
..../application/public/controllers/*
..../application/public/models/*
..../application/public/views/*
It must default to the standard location when you don't organize this way, which causing the collision that you are experiencing.