Around March 2008, the automatic transmission in my Camry died on the highway at 110k miles. :thumbsdown: DH had just left on a remote.
The transmission place in town -- very reputable too -- Quoted $2800-3,000 for the repair. I'd always had standard before, so I didn't know there are no 'new' transmissions made for replacements. They rebuilt it completely with kits. Thankfully I had ext. warranty and 'only' had to pay $350 + rental car for the work.
The company provided a year warranty on the transmission. Which was good considering 4 months later, the transmission died again. 2nd gear wouldn't shift into third for a long time and when it did, grinding resulted.
They redid everything, worked great again. Then I drove it for another 9 months and sold the car for $4500. I never relied on it after that.
I still don't trust automatics, there's way too much that can go wrong with them. Very complicated systems.
You have an '01 with poor engine history AND now the tranny died? Not good.
Have they checked to see if there's any recalls with that make/model? Would that be covered under VW's 100k miles/10 year power train warranty at all? Or do they not have that any longer. Apologies if I"m out of touch.
I don't know if I'd do the work or sell it for what I could get for it. It's a 10 year old car. It's overall worth might not be much more than a new transmission costs, which wouldn't justify the expense and work on it.
Good luck. It's a difficult decision.