Are you communicating directly with the BMW dealership??????? You own the car, the used car lot has no 'legal standing' to permit work to be done or even to have the car touched by the dealership. (They may not even know this, they may think it still belongs to the lot...)
I'd make sure they are doing a full and complete job- new trans, new torque converter, etc. With a written warranty (ie Work Order) IN YOUR NAME.
I'd be OK with an all new BMW remanned tranny with the two year BMW-backed warranty.
Keep it as simple as possible...but no simpler.