Hello Tullyhere,
Thank you for the details of the issue you are experiencing with Wi-Fi on your iPhone, iPad Air, and iPad mini. You have taken some really good steps to troubleshoot this issue already.
I found an article that includes a few additional steps you can try. I recommend reviewing the steps in the sections titled "Resolution" and "Unable to connect to a Wi-Fi network" for the issue you described (you can skip any steps you have already taken):
iOS: Troubleshooting Wi-Fi networks and connections
http://support.apple.com/kb/ts1398
Additionally, I recommend reviewing the following article for recommended settings for Wi-Fi routers:
iOS and OS X: Recommended settings for Wi-Fi routers and access points
http://support.apple.com/kb/HT4199
Thank you for using Apple Support Communities.
Best,
Sheila M.