Connectify Hotspot - The Wi-Fi Software Router for Windows PCs
This might do it.
It sounds like you are using Wifi on your PC to connect to the internet via a distant Wifi router that your wife's Kindle can't reach. Normally a hot spot uses a different connection (cellular or hard wired) to reach the internet and then only uses Wifi to feed local devices. You're trying to use the one same Wifi connection to accomplish both, and that may prove problematic.