Can I make computers in this subnet visible to computers in the main network without merging them?
Yes, as long as the routers offer the necessary configuration options. (Surprisingly many devices calling themselves "routers" don't let you add any routes!)
When your devices on the outer subnet send packets to another network, they first go through their "default gateway", and it's that router's task to route them to the correct next router.
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Assuming that 192.168.1.1 is your first subnet's default gateway, it needs a static route towards the 2nd subnet:
- To network: 192.168.0.0/24 (aka 192.168.0.0 mask 255.255.255.0)
- Via gateway/nexthop: 192.168.1.2
If the 192.168.1.2 router has a firewall, it must be configured to allow connections from 192.168.1.0/24 (or even disabled outright).
If the 192.168.1.2 router has NAT enabled, it should be disabled... but it'll probably work either way, as long as the firewall in step 2 allows.
On the second router, it will need an address assigned from the primary subnet, like 192.168.1.254 and plugged in on the shared network. Traffic will need to be allowed on the both firewalls. Then on both routers you will need to setup a route to each network. All traffic going to 192.168.2.0 needs to be sent to 192.168.1.254. You will need to be careful with DHCP when the two routers are plugged in as both could hand out DHCP requests to the devices.
If your router(s) do not have the ability to do static routes, you will need to replace with a better router or on each computer you will need to manually add a route statements.
From a command prompt you can do the following command.
route ADD destination_network MASK subnet_mask gateway_ip metric_cost
route ADD 192.168.2.0 MASK 255.255.255.0 192.168.2.254
Then on the other side you would need a similar command
route ADD 192.168.1.0 MASK 255.255.255.0 192.168.2.1