LogMeIn Rescue has this functionality
LogMeIn has a product\service that has this ability-specifically their LogMeIn Rescue line of services. You have to pay for it. However, considering that this is aimed at enterprise support, you should consider it expensing it.
Also check out Good Mobile Messaging and their suite of mobile device software\services.
Logmein does NOT offer GUI remote control of IOS devices
Last I checked, and I've been following closely for a while, LogmeIN, nor anyone else I know, do NOT offer GUI remote control of IOS devices. All say its due to Apples restrictions and architecture.. which enforces VERY strict rules about apps talking to other apps.
I find it very misleading that they and several others beat up their limited support for IOS devices to make it SOUND like they have GUI control, like they do for most other devices.
They do offer some good config support etc, but no GUI.
This remains a very major need for IOS devices, both in Enterprise environments, and also in many small personal situations as many have pointed out. I was most frustrated that I could not offer better support for my father during his terminal illness last year when he eventually died of cancer. I was willing to pay a substantial amount for a GUI remote control app to assist him.
rgds .. Peter