I probably can't help much, but I will ask for clarification, so that someone who really knows can help: It starts out fine in 1st gear, shifts into 2nd gear just fine, and then won't upshift into 3rd, is that right? It's important to know on an A4LD, because you only have two solenoids: one to control the 3-4 shift and one to control the torque converter lockup clutch (TCC). If you have a problem with the 2-3 shift, it isn't a solenoid problem.
Maybe a problem in the vacuum modulator, though I would expect a problem with the vacuum modulator to also effect the 1-2 shift. Or a problem in the valve body (sticky valve or something) or a broken band or something.