The VMware vSphere™ vNetwork may be more suitable for your topic.
You can think dvs/VDS/Nexus1000v as a Layer 2 switch.
So if you want a private network, create a VLAN network which is port-profile on Nexus 1000v and will be seen as a dvPortGroup in dvs/VDS.
You need the network to be accessible across 3 ESXi hosts, so on the uplink physical switches where the ESXi hosts are connected you will also need to create the corresponding VLAN matching with the port-profile.
There is no need to create gateway or interface VLAN on the physical switches as you want these to be private.
Then don't you may need multiple Network Adapters on the 3 VMs for the private network.
Bayu Wibowo | VCIX6-DCV/NV
Author of VMware NSX Cookbook http://bit.ly/NSXCookbook
https://github.com/bayupw/PowerNSX-Scripts
https://nz.linkedin.com/in/bayupw | twitter @bayupw