Two Subnets On Same Physical LAN on SBS2003 domain

You said physical lan, as in, both subnets are on some switches ? or you mean, they only "meet" at the server ?
If both subnets are connected through switches, have them all changed to subnet 255.255.0.0 instead of the traditional 255.255.255.0
A route statement on the SBS2003 Server works only if the server itself is a router., but you said gateway is 192.168.0.2 which makes me doubt it.

Correct, the server is not the router.  The 192.168.3.x is connected to a separate switch - just because of distance and only one LAN cable was available - there are 5 devices connected to the 192.168.3.x side.  So do I need to get an appropriate router? Currently they are utilizing a Linksys home type router.

So you've got the same VLAN running two subnets.  It's good that everything is on separate switches as this makes it easy to separate everything using a router.

The Linksys router will do fine for this.  All you need to do is disable NAT on the Linksys router and add a route to the 192.168.3.0 network via the Linksys router's WAN IP to your internet router.

To explain,

The Linksys router will have 192.168.3.1 255.255.255.0 on its LAN interface (for example).  All of the devices on the 192.168.3.0 addresses would use 192.168.3.1 as their default gateway.

You connect the WAN port of the Linksys router to the switch where your server sits, using the cable that links the two switches together, and one of the LAN ports connects to the switch where all the 192.168.3.0 devices connect.  The WAN port of the Linksys router uses IP address 192.168.1.254 255.255.255.0 and it would use the internet router's IP address as its default gateway on the WAN port.

That should allow both subnets to see eachother.

The WAN port of the router is connected to the ISP (Internet) and has a static public IP address. Can't take away from this. So now how to handle?

As you said, you need to communicate between the two subnets anyway (instead of some trust issues, like 2 competing companies), so just use my solution (see first post). No need for extra hardware.

@kimputer: OP says...

I have a vendor that installed some audio equipment that has to be on a separate subnet 192.168.3.x

That means you can't simply change the subnet mask as that would make everything on the same subnet.

"If both subnets are connected through switches, have them all changed to subnet 255.255.0.0 instead of the traditional 255.255.255.0"

So change the subnet to 255.255.0.0 on the switches only? No other devices need this?

Change the subnet mask on ALL devices is what Kimputer was suggesting.

That would be a lot of effort for the 192.168.0.x side.  I have a SonicWall router on order for them which should make the process easier to accomplish. If I could find a solution without them purchasing a new router - that would be great.

Just FYI for one of the post the mentioned vlans - no VLANS configured.

To change everything in one go, just configure your DHCP server correctly. Collect all Mac addresses, and put them all (and configure and assign a fixed ip address) in the reservations list.

I am hoping I can make it simple with a SonicWall Router.  Will update once it comes in.

Just to keep you informed, what Kimputer's suggestion does is actually create a large subnet containing all of the ip addresses you want to use. So in reality, you will only have one subnet, but all machines will be able to talk.

If you absolutely must have two subnets, then you need to take a different approach.

Btw, a subnet mask of 255.255.252.0 would have sufficed. And made for a smaller broadcast domain.

Also, please remove the route statement if you are changing the subnet mask.