Are there remote administration tools for iPad? Preferably screen sharing
I would probably recommend the Teamviewer app for iOS.

Full instructions found here. 

It is Free and you can download it from App Store

For your specific case read this

How to Get Started with Mobile to Mobile Connections!

That will allow you screen sharing but not Control since iOS does not allow remote control at this time. 

But there is an exception.
You can connect to any iOS based devices with TeamViewer for Remote Control for iOS. This feature, however, is limited to connections to apps that have the TeamViewer Screen sharing SDK for iOS integrated.

Therefore, only screen sharing is possible for connections from a mobile device to an iOS app.

On the Supported iOS App

This functionality is based on the implementation of the Screen sharing SDK by the app developer and meant for them to support their app on an iOS device.

Therefore, it is only necessary to initiate a support request from within the supported app.