2 separate networks on 1 computer

Hello,
I have an HP DL380 file server, serving two groups of clients with about 10 computers each.
Both of these groups are on 2 separate DELL Power Connect 2748 switches.
The file server has 2 sets of NIC ports ( a total of 4 NIC’s, teamed in pairs).
I would like the 1st NIC port on the file server connected to the 1st switch with the 1st group of clients, and the 2nd NIC port connected to the second switch with the 2nd group of clients.

This should help significantly with load balancing.

The problem is ALL of these computers are connected to the corporate domain, and are assigned an IP address from the DHCP server.
Both of these DELL switches are connected to a 3rd switch on the corporate domain.

The clients on switch 1 can access the 1st NIC port on the file server without any problems, but the clients on switch 2 does not use the 2nd NIC port on the file server, but instead route through the 3rd DELL switch and back to switch 1 and then finally to the 1st NIC port on the file server.

Is there any way I can achieve this setup described above?

I believe I would need to set a second IP address on all of the machines that are connected to Switch #2? And also the 2nd NIC port on the file server.
The tricky part is that all the computers on Switch 2 must be on the corporate domain simultaneously.

Tomio