Wait, stop, wait. There are a handful of mistaken assumptions here.
The "R" in the 1769-L33E
R means "Ring". The two Ethernet ports on the controller are not separate and unique, but rather are built to support the "Device Level Ring" fast self-healing ring protocol.
These ports are not separate. They have the same IP address. They are not built to be connected to different networks, either physically or logically.
The 1768-ENBT is for use with an older platform; the 1768-L43 and 1768-L45 were a mid-range CompactLogix a few years ago that had a left-side 1768 (not 1769) bus connection for ControlNet, Ethernet, and SERCOS motion modules.
While the Prosoft MVI69 module does provide some data table emulation connectivity, it does not allow you to access tags at random or upload/download or go online with the CompactLogix.
If you want to connect a CompactLogix to both a local automation network and an enterprise network, the best way is to install and configure a network router of some kind.
Rockwell sells a couple of popular ones that also provide "Network Address Translation", so that one or more devices on the automation network appear to have addresses on the enterprise network.
http://ab.rockwellautomation.com/Networks-and-Communications/Network-Address-Translation-Device
There are plenty of other IT-level routers and automation-specific routers on the market as well.