@aziraphale OK then we might have a path forward. Understand I haven’t had to do this before so there may be something that will go sideways on us.
But the concept with split horizon dns is to create an A record entry in each dns server. On the dns server on the staff network you will create an A record fogserver.domain.com (or whatever name you choose) that points to the nic on the staff network. You will do the same for the students network. That A record for fogserver.domain.com will point to the nic on the students network. That way a client on either network will always resolve to an interface on the right network.
Once that is setup now you need to get in and tweak the FOG configuraiton. Anywhere in the FOG Settings that refer to an IP address you need to replace it with fogserver.domain.com. Also in the storage node configuration for your FOG server, replace the fog server IP address with its fqdn name.
Now there is one other place you will need to edit by hand. In /tftpboot/default.ipxe exchange the fog server IP address with the fqdn name.
Understand this setup is not supported by the FOG Project and the next time you upgrade your fog installation, the installer may overwrite certain configurations for you. Most will stay the way you put them.
Now the only gotcha here is that there are some pxe boot roms that that are pretty dumb and will not translate the fqdn name to an ip address because they ignore DNS resolution. You are going to have to try it to see how well this setup works for you. It may be just as easy to setup a second fog server on the students network so you don’t have to deal with this complexity.