Why do your operations people have a problem with dual NICs? It’s a pretty standard arrangement for things like dedicated firewalls. A router is actually 2+ NICs with a computer between, and cable/DSL “modems” are just a computer with an Ethernet NIC and a cable/HSPL NIC. At home I use an old Dell server running Linux with the built-in NIC connected to a cable modem and 3 add-on NICs to connect my other computers to as a firewall/router/web server/ftp server/ICS.
However, if you can’t get around their limitations, you will need them to do the work of setting up special groups and permissions for the outside people to have limited access to the network. You need to have a meeting with the people who want third party access added and the IT people present, so that something can be worked out that makes everyone happy. IT is putting up the barriers, IT needs to come up with the solution.