I hope i understand your issue correctly.
If so then this should be helpful to you...
This is how I have FiOS MI-424WR and external router (RT-AC66R) working together.
My FiOS router is a ACTIONTEC MI-424WR. If you have a different model simply substitute it whenever I mention the "MI-424WR".
IMPORTANT: If you are switching your "main" router (the one that gets address from FiOS, you MUST release IP address before you make another device with different MAC address your "main" router, or you will spend a long time with Verizon on the phone making them release and renew your IP lease!
1. The MOST IMPORTANT part is to have Ethernet enabled on your FiOS box! If you are getting internet through your FiOS router by way of Coax/MoCA then you are doing it wrong.
You will still be limited by the FiOS router and its tiny NAT table and other shortcomings! If you do not have a SEPARATE ethernet line coming out of your FiOS box AS WELL AS a Coax cable, I highly recommend you call up Verizon and have them send someone out to activate the Ethernet port on your FiOS box and run a wire up to your router! It should cost you $100 exactly
. If you are going through the FiOS router as a MoCA bridge than you are getting NO benefits of adding a better router to your network (except on LAN obviously)!
2. At this point you can configure MI-424WR to be a client of your router. You do not need DMZ or anything. Tell your MI-424WR to get a DHCP address from your router. Disable DHCP server and wireless and firewall. I am 99% sure this is all I had to do but it's been a long time.
3. At this point the Internet light on your MI-424WR should be orange instead of yellow. If it is orange even though Coax is plugged in, you are good to go.
4. Set up your RT-AC66R with the Ethernet wire direct from FiOS box to WAN port. Once this works and you have a DHCP address, now you may attach the MI-424WR. Attach ethernet cable to the one of the LAN ports on AC66R and the other end to Ethernet WAN on MI-424WR. You should see the internet light on MI-424WR change color.
5. If you have FiOS TV, turn on your TV and see if TV guide works. If it works, you are all set. If it doesn't, make sure you didn't mess up setting it up
The goal is to have RT-AC66U handle all the "router" functions. If you try to "split up" the work between AC66U and MI-424WR you will have problems. Your DDNS and AiCloud should work fine now, as well as better overall internet performance!
Some details (LED colors etc) might be slightly off because i am writing this from memory. I used to have a lot of trouble with MI-424WR and my routers before until I came up with this setup. It's been running like this for almost THREE YEARS now and works BETTER THAN IT EVER HAS.