So it seems that we have to connect iPhones and iPads on our network... Does an OpenVPN client for the iPad exist? If not, does a similar solution (where we control the VPN server) exist?
There is no official support for OpenVPN on iOS. So unless you want to Jailbreak all your devices, there's no way this is going to work.
Instead, you could setup an IPsec VPN using tools like strongSwan or by buying a commercial appliance. An entry level Cisco ASA isn't that expensive, even more so when considering the time it takes to set up and secure something like this yourself.
An official app for OpenVPN doesn't exist on Iphone/iPad this is due to the apple policy that don't allow to install additional kernel module.
So the only solution for the moment is Jailbreak your phone and download an openVPN client from Cydia...
If you want an OpenVPN connection, I suggest getting a DD-WRT supported router, installing DD-WRT firmware that supports OpenVPN, configuring the router properly and then connecting to that router with your iPad.
There's lots of information online about DD-WRT and installs, and it can turn into a real headache. To avoid future headaches, confirm that the router you buy supports DD-WRT with OpenVPN well - again, through searching online and finding answers.
Should do what you want
"GuizmOVPN is an OpenVPN GUI for iPhone/iPad, designed to be easy to setup, configure and run"
Since Feb 2013, the Open VPN is supported on iOS through OpenVPN Connect. Free and open source app developed by OpenVPN team with permission from Apple
Well, how about a 50 gram router smaller than a deck of cards that runs openvpn?
will get the ipad into a 256bit openvpn tunnel.