Does using lower Isolation Level improve OLTP performance?
SQL Server 2008 Solution

Seeing as you are thinking of duplicating the database into two instances, changing the isolation level from the default Read committed isolation level to Read uncommitted will not have much of an impact.

Reference: Isolation Levels in the Database Engine

The inserts occur on instance1.database which does not have any active (SELECT) queries. 

Transferring the data from instance1.database to instance2.database (Reporting database) will have a small impact during the night. Otherwise the users are not impacted by the INSERTs occurring on instance1.database during normal office hours while accessing instance2.database.

No need to change the isolation level.

Alternate Solution : Availability Groups

You might be better off with a newer SQL Server version (2012 or greater) and Availability Groups. This way you could have your live data sent to the AG and you just configure the second replica to be READ-ONLY, which you then query for reporting purposes. This is documented in the MSDN article:  

Configure Read-Only Access on an Availability Replica (SQL Server)

Here is an overview of the AlwaysOn Availability Groups (SQL Server)