I have an iPhone 4S with
giffgaff (which is part of O2 UK and uses their network) and all the Live services work fine for me, so you should definitely get a connection via your wife's phone.
When you've paired your phone, do you get the network details at the top right of the iDrive screen? Perhaps your local dealer might have an F30 demonstrator you could try your two phones with? Might be worth double-checking your network settings (on the iPhone that's Settings - General - Network - Cellular Data Network), but that's a longshot. Good luck, let us know what the dealer finds.