I am certainly no expert on the subject and don't have any book recommendations, but I used to teach kids art and currently work with kids as a classroom aide. Some kids are just wired this way, but I do think it is something that can be worked on and will benefit them in the long run.
One important thing is to model making mistakes. So often as adults we are only telling kids the right thing to do. It is really powerful for them to see us making mistakes, taking it in stride (or even laughing about it) and moving on productively. Any exposure to this is helpful, though a culture (school, home, etc) of this mindset is the best.
As far as art goes, is there is any way to get DD involved in process driven art? Lots of experimenting and not focusing on the end result might help. I'd also go to museums or galleries that have nonrepresentational art and talk about the importance/meaning of this kind of work - expressing ideas and feeling without being literal, and how some things can be better said this way. In the real art world, creativity is far more important than technical skill.
Some perfectionist kids will always have these tendencies, but I personally have seen some improvements. I can empathize with your mom, and agree if we can instill any amount of fearlessness (artistic and academic, not physical!) it will go a long way