The 'gateway' field of routes has to specify the next hop to forward the packets to. Specifying the current router is not needed (it already has the packet after all) and doesn't provide the necessary information to the route.
(Specifying the current router actually has the specific meaning of indicating that the network would be reachable without going through any further router. That is, you'd use that kind of route if there were multiple IP networks overlapping on the same Ethernet. Since the devices aren't actually there, "Host unreachable" will be the result.)
So if you want to reach the network which is behind Router 2, then the "gateway" or "next hop" for that route would indeed be Router 2 – not Router 1 itself.
Additionally, the "gateway" needs to be an address that Router 1 already knows how to directly reach. In other words, it has to be an adjacent address – in your case, it means Router 2 has to be specified by its 192.168.0.x address (as that's the network the two routers share), and not by its 192.168.2.1 address (as that's currently unknown at the time of adding the route).
So in general, the routes you'd need to add – on all three routers and maybe also on the modem (if anything else besides the routers is connected to it) – would be:
| Destination |
Gateway |
Note |
192.168.1.0/24
(R1's network) |
192.168.0.11
(Router 1) |
(not needed on Router 1 itself, it already has a route for its own network) |
| 192.168.2.0/24 |
192.168.0.22 |
(not needed on Router 2) |
| 192.168.3.0/24 |
192.168.0.33 |
(not needed on Router 3) |
Don't forget to allow the incoming packets through each router's firewall, otherwise even if the packets get there, the router might just block everything by default.
Normally you need to add both R1→R2 and R2→R1 routes for communications to work (one way is not enough). If the routers do NAT, things might start working after just the R1→R2 route, but it's always recommended to rely on routing and not on NAT.
