Yes, change the IP blocks and gateways and turn off DHCP on your 2nd router. Or, Add a second IP to your servers ethernet interface.
First case .. First Router 192.168.1.x with 192.168.1.1 as lan gateway, dhcp left on. Your servers get set to static ip, and set a gateway for the 2nd router's LAN port.
The 2nd router you have to change the IP block to 192.168.1.x common choice is to make the 2nd router's Lan address (and by definition a gateway address) to be 192.168.1.254.
Alternate and probably easier - statically set your servers with their 192.168.100.x IP addresses, with a gateway of your 192.168.100.1 router. You must turn off DHCP on the 2nd router. Add a second IP address to your servers in the 192.168.1.x IP range. The rest of your devices should be set for DHCP and get their ip address from your ISP router.
In the alternate version, both routers would connect to the same switch (again thats why you must turn off DHCP on the second router) and all of your machines would connect to the switch. By nature of the default route setting, and by statically setting your Servers' ip addresses, they will only go 192.168.100.1 BUT by having a second address on the 192.168.1.x network, your other machines would be able to access them.