you should only have one DHCP server running, the one on the core.
DHCP is used to determine if devices appear on the network or not. If DHCP is not enabled on the core, all network based devices have to manually be added via the Web Admin.
The way that I've seen most setups with an existing wireless/router be retrofitted, is that the WAN connection isn't used at all, and all devices are plugged into the LAN side of the router. The DHCP server on the router is then disabled.