|Take back the second router.|
What you needed was an 8 port switch.
You then connect from modem to router WAN port, and then from router LAN port to the designated uplink switch port (some do not have a designated uplink port and will automatically configure any port to uplink)
This configuration gives you three available ports on the router and seven more on the switch. Plenty for future expansion
If you cannot return the second router then connect from router 1 lan port the new router LAN port. Disable DHCP in the second router. In this configuration you have three available ports on each router.
Note: The cable between router/switch or router/router may need to be a crossover type unless one or both devices has auto sensing self-adjusting ports. Most do.
Goin' Fishin' (Some day)