Is this an MVC application where the live site is the public one, and the admin interface is just restricted?
CI is only needed on the admin part, but actually only meant for development... so not recommended to keep running on production.
If it's MVC both applications (live site and admin site) connect to same DB anyway so only 1 restore is enough.
In regards to having 2 instances behind a load balancer, you'll need to name the instances:
Add the following (with different value on each) to the app settings section in each of the web.config files on both nodes
<add key="CMSWebFarmServerName" value="xyz" />