JB Weld? Yikes.
The key to re-sticking your VW moulding is preparation. First of all, pick a nice warm day to do it. Second, you *must* remove all traces of the original 2 sided tape (the factory uses a foam 2 sided tape) and thoroughly clean and prep both surfaces (the moulding pieces themselves and the body panels where it will be stuck to). Prep-sol works extremely well for surface prep - it leaves no residue. Most prepping agents will eat into plastics, so be careful when using the stuff on the mouldings. If you don't throroughly clean and prep, or if you use anything that leaves a residue behind, then your mouldings will just come back off. If you use the good 3M stuff (available in larger rolls at Robbins Auto Parts stores) and take your time cleaning and prepping, then there's no reason it shouldn't last as long as the original factory stuff did.
If you're completely fed up with the moulding on your A3 VW, and absolutely never ever want to deal with it sagging or coming off again, then buy the clip moulding kit, which includes all new moulding pieces and uses clips that snap into the holes that are already in the body and doors of the car. That is what VW should have used in the first place, IMO. The new pieces are a textured black, so if you want to have body-colored moulding then you'll need to have them painted. Here is the 4 door clip-on kit:
http://www.parts4vws.com/catalog/pro...er=1HM898700NF
and here is the 2 door clip-on kit:
http://www.parts4vws.com/catalog/pro...er=1HM898500NF