Two ESXi host servers connected to eachother's second NIC

Solution 1:

On each ESXi, create a new virtual switch based on the direct connect NICs.

Using the 'Configuration' tab in vCenter on the ESXi, select 'Networking' and 'Add Networking...' Create new 'Virtual Machine' connections. Create a new virtual switch, and associate that switch with the proper NIC. Give the switch a meaningful name -- you'll need it later.

Now, in each VM that needs to talk to over the direct connection, create a new NIC (or modify an existing one), and set it's 'network label' the the switch you just created.

Assign the private IPs to those virtual NICs. Programs running in the VMs that use the private IPs you create will be routed across the direct connect.