<<< Isn't the RP614 an ADSL router rather then just an Access Point device? >>>
I think what is required is a "Cable/DSL Router" that can connect directly by ethernet cable to one of the LAN ports in the "ADSL Modem/Router". That way, the second router will get a LAN address allocated by the DG834 as its WAN address and it will in turn allocate further LAN addresses to its own "client" PCs.
It is important that the routers operate in different Subnets - if the DG834 uses the 192.168.1.xxx subnet, the second router needs to operate with a subnet whose third octet is a value other than "1", e.g. 192.168.2.xxx
The way to prevent the two workgroups from communicating is to keep them in separate subnets.