The better architecture is to have the routers exchange places. Have the FIOS router first, then the Verizon behind it (LAN to LAN, never use the Verizon's WAN port) merely for additional ports (and have its DHCP server disabled as well).
I don't use Verizon's WAN port, and I can't switch the router's places because the Verizon one has the Coax "port" which I need for the Internet to work. Unless I'm missing what you're saying.
Can you explain a little more please?
Well let's back up a second. I assume this is FIOS broadband, right? Wouldn't FIOS use the FIOS router, or are you saying that FIOS actually uses a COAX connection for the broadband connection via the Verizon, then fronts it w/ a standard router they just call their FIOS router. I don't know, I've never used FIOS.
If that's the case, then fine, leave it that way. But those ports on the Verizon shouldn't be used except to connect to the FIOS. You can't connect anything else to the Verizon even though it's tempting since those ports are on the WAN side of the FIOS!
This is no different than someone who has a dsl modem+router, then wants to continuing using it as the modem, put substitute their own router. You place the dsl modem+router in bridge mode, then patch it to your own router, LAN to WAN, respectively. But once you do, those other LAN ports on the dsl modem+router are OFF LIMITS! At least if you expect to gain access back into your local network. If you were to use those ports, any DHCP requests would go to the ISP, not your router. IOW, as configured, you have to treat the Verizon exactly as you initially described it -- as a MODEM! But you violated your own statement when you decided to grab some of its LAN ports for extending your local network. NO NO!