iPhone Personal Hotspot Troubles

The AT&T iPhone “personal hotspot” just doesn’t work with our iPhones.
The other day I wrote about my new Nexus 7 pad. It’s wonderful.
For travel with the pad I need wireless. So I switched my iPhone’s AT&T plan over to the one that lets you use it as a “personal hotspot.” This makes the phone into a device that receives cellular data and acts as a wireless router to which you can connect your computer and other devices.
It worked for about a day. Then it stopped working. I went to the Apple Store, they couldn’t figure it out and gave me a new phone — which also wouldn’t work. At the store we called AT&T to get things started on their end. So the next day I spend about 4 hours on the phone trying everything, and they gave up and “escalated” it.
(My wife’s iPhone 4s worked, mine is an iPhone 5 — she hasn’t updated the OS to the one with the terrible maps.)
About a week later AT&T said they had it fixed. And it appeared to work — for a while. Now it only works once in a while, maybe 20% of the time. And the thing is, now hers only works about 20% of the time as well.
SOMEtimes I can trigger the hotspot to work by plugging my iPhone into my computer with the cable, which makes it work over USB and for some reason some of the time that turns on the wireless hotspot so the Nexus 7 sees it… But only sometimes.