Not how it would work. The device needs both 192.168.2.1 and 192.168.1.2. if it only has 192.168.1.2 the traffic might get there but then it can't be passed to the end device on the 192.168.2.0 network because there is no interface. It would need 2 different lan interfaces one on each network......that again is what makes a real router a router.Turn dhcp off on 192.168.2.0 and 192.168.3.0, assign a static IP to the router of 192.168.1.2 and 192.168.1.3, remove the cables from the wan of 192.168.2.0 and 192.168.3.0 and put them in the lan. Done.
So what I was telling the OP to do was to flatten the network and use the other routers as just switches.Not how it would work. The device needs both 192.168.2.1 and 192.168.1.2. if it only has 192.168.1.2 the traffic might get there but then it can't be passed to the end device on the 192.168.2.0 network because there is no interface. It would need 2 different lan interfaces one on each network......that again is what makes a real router a router.
There are ways to do this using subnetting, but most of the times it is done using vlans or physical lans (if you want air-gapped security).that's is the configuration I had, but I was trying to totally isolate the different networs since one section will be dedicated to security cams, other for games, and so on. And I didn't want to put the control in only one router, seems to be I am going to need real routers as you say.