It is impossible to do what you ask.
The modem has to work as router for it to use wireless.. It therefore has to be the main router on the network.
The Airport Extreme can be used in static IP mode with DHCP turned on.. that means it controls the clients that do connect to the AE itself.. but it can never control the clients on the Arris.
Static IP setup is here.
Re: airport time capsule keeps disconnecting
NOTE.. you might find instructions saying to bridge the Arris.. (that may or may not be possible but lets pretend it is).
People will suggest you double link the Arris LAN to AE WAN port.. and then Link AE LAN port back to the Arris LAN port.. and with some judicious juggling of IP addresses you will end up with a happy compromise.. but just look at the wiring.. it is like feeding the engine exhaust back into the intake. It will run for a while and then a change of IP will trigger a network collapse.