What do you mean by default vlan? Is that the switch management vlan, or vlan 1? Or is it the native vlan? If it is vlan 1 or the switch mgmt vlan, I would move the domain server onto another one, as cisco cat switches can have performance issues with devices on the mgmt. vlan during high traffic loads.
You can allow the student pcs to connect to the current domain controller by coding the proper acls - for active directory I believe that port 445 is used as well as ports 137-139 (tcp and udp). I am not sure about port 135, it may be needed too.
However it is best to have a seperate domain controller on the student vlan, to mitigate against some direct attacks by the student workstations directed towards domain services.