I believe that your initial problem was a shudder from 2-3? If so and if there are no other codes indicating a more serious problem, the cure is one solenoid called the STH solenoid and there is a Volvo dealer TNN on this.

Volvo dealers don't ship their GM trannies to a GM dealer, they use Volvos reman. program and they're rebuilt at a place that does nothing but rebuild trannies, etc. Volvo doesn't attempt to teach Volvo techs how to rebuild their Auto trannies, never have, so that's why your trans will never be opened up and rebuilt at any Volvo dealership. At GM dealerships, GM teaches their techs how to rebuild them simply to keep costs down and also due to far more #s, volume of cars on the roads compared to Volvos 1%.

If you really want to know internal specifics, you can probably find that out by visiting GM tech related forums.

With Volvo, if it's not a software or STH solenoid due to codes and further diagnostics (and yes, there are ways to know), there are usually codes which specify where the problem is and some codes mean internal sealing problems thus "new trans" as far as Volvo is concerned.

If in doubt, get another opinion from another Volvo dealer. I wouldn't advise any tranny shops.