Your 2002 MINI One has the Rover Midland gearbox which can have several common problems, (search on MINI2 forums for "Midland" and you will see them)...............although I have not heard of jumping out of 2nd gear being a common fault?
Hopefully it will turn out to be a cheaper fault in the Gear shift cables or mountings area rather than an expensive gearbox internal fault.
What mileage has the MINI done?
i hope its something cheap aswell!!
its got 85k on the clock but it has been well serviced, she has spoke to the garage she got it from as she has only had it 3 months, they are taking a look at it tomorrow.
It was fairly common fault with the early ones i had a dec 2001 mini 1 & it needed a new gearbox in 2002 it was warrenty then & most cars got fixed for free ,some cars probably slipped through the net ,minimania in wales do some kits to fix the problem