Use second router from Cable router IP 10.0.0.1 ?

[Geek-9pm]

I need to extend my local network Wi-Fi  further.
The Cable router has a IP set at 10.0.0.1 and no way to change it.
Bu I want to use another router to put Wi-Fi at tieback of my property. We ran a long CAT 5 cable to a D0Link router that is on 192.168.0.1 ad it almost works. But something is not right. Netflix gets an error.
I have never understood why the do the you the 10.xxx.xxx.xxx  range on that router. Most common usage here in the USA is the 192.168.XXX.XXX IP for home network. I read somewhere that all devices on the same network must be in the same subset. So I am confused. 
Is there a way to deal with this? Or should I just go buy a cable modem and use a standard routers? I have old Wi-Fi routers that I can use. A simple naked  Motorola Cable modem is about $35 on eBay and they claim it can do the max speed now used by Comcast. I wonder if that would be the best way to go?
Any ideas?

[camerongray]

You generally don't want to chain multiple routers like that. Instead to extend your WiFi you should be using a plain access point rather than a router.  You may be able to set your router up as an AP if it either has a mode for it or you can bodge it by disabling DHCP on the second router, connecting to its LAN ports to your main router rather than the WAN port and setting the IP of the second router to be on the same subnet as the main router.

[Geek-9pm]

What you say is what I am trying.
But the bottle neck  s the Comcast router is stuck on the 10.0.0.1 local IP and there does not seem to be any way  to alter t.

I am going to buy a cable modem/router that works the way I want.