You can't replace a modem with a router...you need both, unless you meant replace the connection to the computer with a router which is a good idea provided you can find a router which accepts a USB modem connection.
If your ISP can provide you with an Ethernet modem, than get that first and not only save youself some money, but it will confirm that the USB modem is the issue in the first place. Although, my personal opinion is that probably it is the USB modem causing the kernel panics.