Is your mini an auto or manual? Also what year is it? I towed my 2005 many years on a tow dolly and never had a single problem. I now have a 2008, only towed it once but had a few problems. First is no steering lock. On the Kar Kaddy you have to lock the steering. I solved that with bungee cords but it was not easy to find places to hook them to. Second problem was I had anti lock brake errors when I pulled it off the dolly. After I parked it and went to drive it again they were gone and I have not looked into what happened.
Ralph
2006 Sightseer
2008 Mini Clubman