This sounds like a classic scenario for content mirroring.
Website1 would be the source site, and website2 would be the target site. 

Note that mirroring in CMS 6 requires Enterprise licenses.

Here are some good resources on mirroring setup:

• https://andersnordby.wordpress.com/2013/01/14/setting-up-mirroring-2-0-in-a-cms-6-r2-environment/
• http://epiwiki.se/configuration/setting-up-mirroring-2-for-episerver-6

Other options could be:

• Exposing your content from website1 as an RSS feed and consuming the feed on website2.
  This way, content would be maintained at website1, and website2 would just read the content - it would not be imported into website2.

• Implementing a custom page provider to share content from website1 to website2. 
  This way, content would be maintained at website1, but the content would be shared to website2 and would appear in the page tree as if it was part of the site.
  Custom page providers also require Enterprise lisences.

thank you very much Arild.

While trying to run mirroring, i got the below error

The job failed: Exception has been thrown by the target of an invocation. [
Error executing task "MirrorChannelSource": Failed to connect to database using connection string with name 'EPiServerDB' (Format of the initialization string does not conform to specification starting at index 0.) 
]

I provided the db user crdentials while installing mirroring. The user has access to both the source and destination cms db.  Please advise

Most likely a malformed connection string. Look for extra quote marks or similar.

Have you double checked that the server name (or IP), database name, username and passwords are correct? Can you manually log onto SQL Server using the info from the connection string?

thanks again Arild 

There was problem with connection string. After fixing that I came across the below issue

The job failed: Exception has been thrown by the target of an invocation. [
Error executing task "MirrorChannelSource": Value cannot be null. Parameter name: type () 
]

googled and found that the above error is due to missing dlls. http://world.episerver.com/Blogs/Shahid-Nawaz/Dates/2010/10/Setting-up-Mirroring-20-in-two-ways/ 

copied  dlls from my episerver source site to mirroring service  bin.... but it didnt work ...I am still getting the same error...Is there anyway to find the actual error?

Well it sounds like you are still missing some DLLs. Did you copy all of them from the source? Are the sites using the same EPiServer build version?

thank you so much Arild! I have completed setup... cheers :)