[mipearson]

I'm a bit stuck. Bought a 2008 X3 3.0si with 110,000km (~70k miles).

Drives fine during the test drive. I do all the usual things - hard accel, soft accel, soft braking, hard braking, full left/right lock, etc. Seller arranges for it to have a couple of things fixed up (coolant leak, transfer case fluid) as part of roadworthy.

I pick it up a week later and five minutes later it starts to "bunny-hop" as if it's a manual with a learner driver as I'm getting up to speed. At this point I begin to suspect that I've bought a lemon.

(also for those comparing prices - labour & parts are much more expensive in Australia, in general)

Long story short:
(a) automatic transmission specialist shop close to me believes it is *probably* but (not 100%) the torque converter, will cost minimum $2k to pull the transmission out & send the converter off for a recondition. If that doesn't work - a new transmission would be ~$6-7k (inc labour). However, he mentioned that the transmission fluid didn't look as bad as it would normally for a cooked converter (or transmission), and that torque converter failures on these are relatively rare.
(b) my usual BMW mechanic (recommended to me by the 1 series forums here) took it for a drive with me and is completely stumped - would need more time with it, but he's a good distance away
(c) after confronting the seller (as having a car drive differently after you buy it is a bit suss), he got on the phone to the mechanic and got them to agree to cut-rate labour to fix up the problem. They want $2k for a second hand transmission, then probably a bit more for the labour, but it's all a bit suss as they were diagnosing this with me over the phone, and I have worry that they screwed something up when replacing the transfer case fluid which is causing all of this.

Other symptoms:
* problem gets worse under heavy driving - and I live in the hills, so all driving is heavy
* also has trouble working out which gear it should be in: think clutch slip like symptoms when accelerating from the lights, and it staying in an innapropriately low gear occasionally. Car has been driven at least 400km since the fluid change & the computer was told to reset.
* occasional whirring or grinding sound from under the seat, where you'd expect the drivetrain (but not the transmission) to be
* when the problem gets *really* bad, the 4x4 traction light flashes on as if it's losing traction

Tires are fine, same tread on all wheels. No idea what to do next as I feel like this doesn't fit under the usual set of problems when a torque converter fails.

Edit: have also disconnected the transfer case, as recommended elsewhere. No change.