|That is one craxy, complicated setup you have there.........and it doesn't need to be.|
As has been mentioned already, you extend with switches, not routers. Client DHCP requests will pass through a switch (or multiples switches as the case may be) and get to the DHCP server on your router without any trouble whatsoever.
Also, you probably have too darn many devices setup. Unless the length of cables between your router and the endpoints exceed 85 meters, you don't even need a switch. Over 85 m the signal can, and often does, start to attenuate so I prefer to keep inside 85 m. Anyhow, that's the only time you'd need a repeater is if you exceed maximum cable length.
What you should have is a 16 port switch connected to your router and all network cables terminating in the same room and jumpered from the patch panel into the switch. If you have a situation where you need to exceed 85 m, then, and only then, would you put another switch (not a router) or a network extender in place.
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.