You stated the answer to your question in the question itself:
Internet Connection Sharing (ICS) technology in Windows refers to a technology that you may recognize as one of many different terms:
Network Address Translation (NAT),
Local Area Network (LAN),
private subnet, or even
router. In essence, when you tick that checkbox to enable ICS on the USB adapter, you are making your computer a router.
Problem is, you already have a router.
It is possible, though unnecessary, to "chain" two NAT subnets together. Instead, I would recommend that you don't try to do this at all. The ideal setup is to have all of the clients (including your own computer) belonging to a single private subnet. For example, if your computer is 192.168.0.1 on the private subnet, all the other clients would have IPs like 192.168.0.2, .3, .4, etc.
Bridging is a technology that joins two networks together at the physical and link layers of the OSI model. Bridging your USB adapter to your router interface (assuming your router interface is ethernet or Wi-Fi) is not only possible, but it is recommended.
An overview of the steps I'd recommend:
- In your router configuration site, disable NAT and DHCP. Now the router acts as a layer 2 switch, which means that the physical and link layers of the Wi-Fi and ethernet clients are joined together, but the router does not create its own private subnet.
- Make sure that if your computer is connected to the router by ethernet, connect it to one of the LAN ports, and NOT to the "WAN" or "Internet" port.
- In Windows, create a network bridge between your USB adapter and your ethernet/WiFi adapter.
- Enable Internet Connection Sharing (ICS) on the network bridge device on your computer.
The essence of this setup is that your Windows computer creates the private subnet/NAT/LAN and provides its own DHCP/DNS services to the clients, and forwards all traffic bound for the public Internet through your USB adapter. Your Windows computer, in effect, uses the Wireless Access Point and Ethernet ports of the router as "additional ports" that may as well be physical ports present on the laptop or a wireless access point built into the laptop. Your laptop becomes the internet gateway, rather than the router.
Do you need more details?