Pings across such LANs are problematic since the 192.168.x.x space is considered non-routable. Source (many): https://stackoverflow.com/questions/528538/non-routable-ip-address
So for this to work your routers would either just work (luck) or you begin a course in routing. Some new to this get upset that there is yet to be a "do this" answer (I do have one below) to fix the routing tables. But as there are some thousands of router models and not all allow routing table work, this is usually a dead end with an upset client.
-> That said, why isn't this a single LAN? For me I set my extra routers up as WAPs (wireless access points) and don't have to invest time into tables and when the router is a P.O.C. seeing if I can install some Open Source Router Firmware.