I need a little clearer picture of your home network setup.
Here is my assumption:
You have a wired signal coming into the house.
It is connected to a cable modem.
The cable modem is connected to the wireless router.
The computers are connected to the wireless router via wifi.
Every now and then you get an IP address conflict.
So, all of that IS your home network.
The wireless router acts as a DHCP server, giving out an IP address to every device that wants to connect to it.
The router does not need to connect to any wireless signal, it is the device GENERATING the wireless access point signal.
If there is an IP address conflict, both of the devices configured with that address will be knocked off the network.
There needs to be a direct wired connection between the modem and the router.
Let me know if you are having difficulties with any of this.
However, I believe your network just needs to be wired correctly.
You appear to be offline.
In the mean time I will switch this to a Q&A format question so you can come back to it at any time. I will also be notified when you make a posting.
Not sure if I need to start over - as I hit the accept button by mistake