A dog is a wonderful experience and a great "bonder" in the family, but it's also a lot of work and requires serious commitment. Proper training and very consistent behavior from ALL family members from day 1 is super important. The best thing you can do is to create a plan and stick with it. Dogs need (and love) consistency, even more so than children :-)
If none of you has previous experiences with living with a dog (either as an owner or as family member or room mate of an owner), you will need to learn a lot yourself and you should be prepared to do so. There is plenty of good learning material and I suggest reading or watching some of it. You can also "ease in" to ownership. Take a friend's dog for the weekend, go to your local dog pound and offer dog walking services (which they often desperately need). Relate what you have learned to the actual behavior you observe until you think you have the hang out of it.
my daughter (8) was lightly bitten in the face by the mother dog
That's very unusual especially for a retriever. It depends a bit on how your daughter felt about it. If she is still excited to get a dog that's really a good sign. This event is an example why training (the dog and yourself) is so important. Almost all dogs will let you know that they are unhappy with something before they become aggressive and a lot has to go wrong before they actually bite. It's quite likely that the dog told you to back off and you and/or your daughter just didn't understand it. Maybe you got too close to a puppy without the mother's permission or the dog just wanted to play. It may be useful to get the breeder's feedback of the incident.
the parents have learned that dogs can be unpredictable.
Wrong lesson: Most dogs are very predictable IF YOU KNOW HOW TO READ THEM. Which, I guess, in this case, you didn't.
(a certified Golden Retriever).
Certification has nothing to do with whether a dog is a good fit for your family or not. It's all in the personality of the specific dog.
That's another benefit of walking dogs from a shelter for a while. You can interact with a bunch of different dogs and see what you like and what not. Maybe you click with a dog and you meet your perfect pooch there (we did).
Is this part of the "residual risk" that comes with having a dog?
There is a residual risk in everything you do. Driving a car, going to swim lesson, riding a bike, etc. The same goes for dogs. Dogs biting a family member is really quite rare, but there are other things that often go wrong with dogs : they might get into a fight with other dogs and accidentally bite you if you try to break up the fight, they run across the street, they will chew and scratch up your stuff, make the occasional mess, etc.
The daughter is very keen on having a dog,
If that's the only reason then this may not be enough. If you and your partner aren't genuinely excited (at least a little) about having a dog in the house, this could quickly turn into resentment and frustration. A dog IS a lot of work and a lot of the work (and money) will come from you despite your daughter's best efforts.
We got our first dog (who has a wonderful dog for us) from a dog pound. A family had gotten her as a puppy since the "kids wanted a dog". However, they quickly found out they were in over their heads and than dumped her at the shelter (where we found her). Don't be that family. Make sure you are fully prepared and committed to doing this.
There is no perfect answer here. A dog is a fairly high risk/reward proposition: it will make you and your daughter very happy but sometimes it will make you also stressed, frustrated, and sad.
my daughter
andthe parents
. 'My daughter is brave, but the parents are somewhat frightened' I'm not clear if you are frightened, or somebody else ? For me it's jarring to read