A homegroup is different from a network identified in the network and sharing center as a "home network." From context, you're talking about a home network rather than a homegroup. To rephrase your issue using normal terminology, network recognition on your Windows 7 PCs is misidentifying your home network when your Xbox is connected.
What happens if you plug your Xbox directly into your wireless router rather than bridging it through your PC? It shouldn't happen, but using bridge mode might be confusing your other Windows PCs.