Samuel Sieb:
If you can't disable the wifi on the modem, then you can just ignore it. Connect the WAN port on your router to the ethernet port on the modem. You end up with double NAT, but it should still work.
Bob Goodwin:
Yeah, I think it's a poor design for the application, I found no way to shut it off.
It's usually called bridge mode. You could see if there's a factory reset option, then see if there's a guided set-up process that asks you what mode it will operate in.
Another option could be to set up a DMZ on their router pointing to yours. NB: Your router absolutely must be between them and the rest of your LAN.
We have been connecting to the WAN on my router. All they have is what appears to be two identical Ethernet portss on the modem-router, both seem to work for conncting my Ethernet LAN. However I have not been able to pass that data through my router to the LAN or the wifi signal. Their wifi signal is what the iPhone and iPads are using now ... I may be doing something wrong in the security configuration?
Did they set up their equipment's SSID with the same name as your own? If so, that'll make it harder for you to manually select yours. Try renaming your own SSID, and select the newly named WiFi network.
Another issue will be the networking addresses. e.g. If their equipment uses the 192.168.0.0-255 range, then change yours to use another range, such as 192.168.1.0-255, or 10.0.0.0-255.
NAT through NAT *can* work with them both set using the same network, but it's asking for trouble, something's highly likely to get confused.