"Unfortuanatly both devices will not connect to eachother over Bluetooth. Neither the iPhone or the iPad will detect the other device."
This has never been a feature of iphone or ipad.
"If I connect the iPhone with my TomTom Carkit it will make a connection without any problem.":
This is a feature.
"Also when I connect the iPad with my Kensington Bluetooth keyboard it makes the connection without any problem."
This also is a feature.
"I even can connect my iPhone with the Kensington Bluetooth Keyboard to type text into the iPhone."
Still a feature.
"Anyone have a solution for this ?"
There is no problem to solve. it is simply not a feature of the devices.
Bluetooth is supported for stereo headsets/headphones, handsfree telephone devices/headsets, some peer-to-peer apps from the app store, some keyboards, and internet tehering where provided by the carrier.
Are you following the directions in the App Store on how to connect the two devices? You might also try turning BT off and then back on to make sure they are not paired with another device then follow the instructions for the GamePad app. You are using the PAN profile which will work for this process and is a feature of the iPhone and iPad.