iPhone 13 keeps disconnecting from my internet, but automatically connects to other homes that I frequently go to

It sounds like there might be an issue with the network settings on your iPhone 13. Have you tried resetting the network settings on your phone? This can sometimes resolve connectivity issues. You can do this by going to Settings > General > Reset > Reset Network Settings. Just keep in mind that this will reset all network settings, including Wi-Fi passwords, so you'll need to re-enter them afterwards. If the issue persists, you may want to contact Apple support for further assistance.

If your iPhone is up to date on software updates, this may be a hardware issue that requires your iPhone to be repaired. I had this issue with an iPad before. Does cellular data work?