How can I configure network to support two IP subnets?

Hello EE!

Ok, here goes!  

Our company has recently migrated our domain to the new company's network overseas.  Currently, all traffic (internet, email, mainframe) goes through our new company's domain over a T1 via MPLS.

We are also implementing a new time clock system for employees to punch in and out from.  The problem is that the latency between here and our new company is causing about a 10 second delay in response to an employee swiping their card on the new clocks.

So, we have a cable modem where the test clocks are connected to via the Linksys SR2024 unmanaged switch.  

What I would like to do is piggyback the cable modem's connection on our new network and keep the clocks on a separate subnet (10.1.10.x vs. 10.1.17.x).  The problem I'm encountering is that I've got to transverse the fiber optic cabling and then configure the remote switches that will directly connect to the clocks.

I wasn't sure if I needed to create a VLAN or perhaps someone might know of a better solution?  If VLAN is the answer, I could really use a high level overview of VLANs since I've never set one up before.

The goal is to decrease the latency to 2-3 seconds which has been proven already in our test environment.  I'm pretty sure that if I configure the 4208v1 correctly, I could do away with the Linksys SR2024...

Anyway, I've attached current and proposed diagrams which will hopefully help make what I'm saying a bit more clear.  

Thanks in advance for your assistance.

Getnoldfast
TIME-CLOCKS---NETWORK-SETUP-Curr.jpg
TIME-CLOCKS---NETWORK-SETUP-Prop.jpg