After taking the transmission out of the 1996 A4 2.8 Quattro auto, it was opened for inspection by my local trans shop.
The fluid was milk coffee brown. They said water had gotten into it, likely by a leak of the trans line running through the radiator.

Likely, it will be cost prohibitive to rebuilt the trans.

I haven't checked, but I thought the car has a separate air to fluid transmission cooler? Or are the 2 coolant line from the trans indeed running through the engine radiator (and a leak could force coolant/water into the trans circuit)?

 

Looks like the radiator is doing double duty as engine cooler and transmission cooler.

Option for me seem to be:
- new radiator (as stock)
or
- flush and use current radiator for engine cooling, install separate new transmission cooler (in front of condenser?)

Is the internal failure of the trans cooling lines in the radiator common (I don't want to get such a leak with the consequential wrecking of the trans again for the next few years)?

Also: since coolant/water got into the trans through the leak, did trans fluid get into the engine coolant circuit? How can I tell? And if so, can (or has it done) harm to the engine?

Naturally, I will flush the radiator and the coolant system. But will flushing with water get rid of any trans fluid that might have found its way into the engine?