As a best practice switching information is not supposed to travel over WAN. To configure a Router-on-a-stick, have VLANs on switch1 connected to router1’s Ethernet port. Similarly have VLANs on switch2 to router2’s Ethernet. I am hoping that both the routers are connected by WAN ports. Now on both the routers you need to configure sub-interfaces and enable routing between the two sub-interfaces. These sub-interfaces will be the default gateway for the respective VLANs. Once you are able to ping between the VLANs between routers, you can configure your VTP servers and clients.
Hope this helps.