Good luck and please update on the progress!
Sorry to hear of the issues with your mom's watch. Just a couple of things. If the watch were a certified chronometer, which it is not, an acceptable deviation in time is -4 to + 6 seconds within 24 hours. The Ballon Bleu is not a chronometer therefore its accuracy and the deviation in time will be larger than that. Also it its possible the watch became magnetized, ...do not rest the watch on speakers, on or near clock radios or cell phones, or if working at a hospital stay away from the MRI department - as they can magnetize the movement which can cause it to be come inaccurate (although its relatively easy to fix this).
In addition, many automatic watches that start out running fast by a few seconds a day do slow down a bit after a few months to a year of normal wearing, as they start to break in a bit. You can have a watch regulated, in which case they open the case back take a screw driver and adjust its rate. Its very simple to do, but you have to open the watch to do that. Its no different than opening the hood of a car to make an adjustment to the engine. Or if one is not happy with that one can replace the movement. I'm not sure I'd worry so much about devaluing the watch as women's watches generally don't hold there value as well as men's watches and they rarely if ever appreciate because their just are not as many lady watch collectors.
I don't think you will get very far with a law suit or anything of that nature, although I don't know the laws in your Australia. However, here in the US, for example if it were a car, you would have to give the company/dealer at least 3 opportunities to correct the problem. If you/your mom won't let them open the watch to make any adjustments, how can they fix the problem? If you had a problem with a car and you told them they can't open the hood to do anything, then technically you haven't given them an opportunity to fix it. Also, it may have been a better idea to give them a chance to open it and regulate it or fix it earlier on when your mom was unhappy with its performance. Then you could say that you gave them every opportunity to repair/fix it and its still not running properly, and you think they should replace the watch. Now that she has had and used the watch 6-7 months, you haven't given them an opportunity to open it and make any repairs, so its less likely they will replace it.
I currently have 12 nice watches, 3 are Cartier watches (2 are automatics and 1 is a manual wind) and I've not had any problems with my Cartiers. The oldest of them is 15 years old, its been in for service when it has needed it roughly every 6 tears or so, and customer service has been very good. I think it is important to remember you have only heard from a handful of people here who have had problems with their watches, and the people on this forum are a very small segment of the market. Cartier sells something like 600,000-800,000 watches per year. So the handful of problems we are reading about here, may be upsetting, but its a relatively small number of problems relative to the number of watches sold. In addition, if you read watch forums for Rolex, Patek, Audemars Piguet and other good brands you will see that no brand is immune from producing a few watches that are far from perfect.
Anyway, wishing you and your mom all the best with resolving your watch issues and I hope she will have a watch free from problems soon. Cheers!