networking - Router Behind A Router

My condo building provides wifi. However they have a stupid terms of service window you have to accept before getting access. I wrote a script that can post automatically to that terms of service window and grant access. My problem is I can not connect my Apple TV as it does not have a web browser to accept the terms of service.

So I took a Raspberry Pi and made it a NAT router. I connected the wifi of the PI to the condo wifi. I put a cron job in place to run my script to post to the condo router to keep the terms of service active. Everything works great until I attached an AirPort to the ethernet. My plan is to create my own WiFi network using the Raspberry Pi as the router and the AirPort as he secondarily router (private wifi network).

So more or less there is double NAT going on. The condo router is doing NAT. The AirPort is using NAT.

After about a minute of use everything shuts down. I think the condo router is blocking us. The condo router will not route packets to the web. It will not give me an IP from DHCP. The condo router is a WatchGuard product.

Is it possible that the condo router is detecting the private network (AirPort) and blocking my access. I assume they are detecting it via the double NAT that is going on. Is there any way to fool the router into not detecting the AirPort and letting all this work?

Thanks.

~Spicer