networking - Running own DNS in intranet, how to reach outside DNS from clients

The Scenario:

I am creating a Network for 8 Windows 7 Workstations running in a Student Laboratory. They are supposed to browse the internet, but not to be reached from outside their intranet.
To achieve this, i run an Ubuntu 14.04 server with 2 NIC's. One NIC (em1) is connected to our department VLAN, i.e. the internet. I'm routing the Workstation-intranet to NIC em2 via IPV4 forwarding over iptables' MASQUERADE feature.

Schematic:

internet
|
departments VLAN
|
Ubuntu server / iptables
|
Switch-------
|  |  |  |  |

W  W  W  W  W ...

After some hiccups, this works fine, see my other post for the full picture (and some of my configurations):

askubuntu

The Ubuntu server is the only machine with a valid IP from the VLAN and needs to use the departments VLAN's DNS servers, or it can't reach the internet.
As i found out via my other post, all the clients need to use our departments DNS servers as well, as their packages run via the Ubuntu router and are masqueraded as packages from it.

The Problem:

Now, i want to deploy an Microsoft Active Domain Controller via Samba.
But:
I need to run my own DNS in the intranet to use all the cool features from a Microsoft Network. The hostnames need to be resolved for Virtual Disks, Log-In, group policies etc.. If i do so, however, the machines will not be able to use the outside / departments DNS anymore and therefore can't request packages from the internet.

How to solve this?

Can i use the departments DNS to resolve my hostnames in the intranet? (Probably not, right?)

Is there a way, that my workstations get their name from my DNS, but request internet packages from the outside DNS to be reached under the same IP?

Is this, why there are usually two fields for DNS servers?

Can i "re-route" the outside DNS parallel to my own DNS into the intranet?