border collie growls and bites

Question
Hi,
I have an 8 year old female spayed border collie.
that shares its home with a 6 year old female lab.
2 boys of 10 and 12 myself and my wife.
the collie has always growled at other kids and strangers either on the street or at home. she also aggressively nipped a couple of kids when she was under the age of 1 causing scratches and bruising.
we spent money on dog doctors etc but in the end they said be careful and dont trust her.
Anyway we kept her away from other kids unsupervised. and apart from the growling she has been fine for about
7 years until last week she bit a 10 year old girls arm whilst the girl pulled her by the collar away from the door and she bit a 10 tear old boys hand whilst the boy was eating food. both times were unsupervised. (I know she should not have had a chance to do this and will never be left alone again with kids and food) the bites never draw blood but do dent and bruise.
my question for you is do I just carry on as I have been or can you suggest a solution.  

Answer
It is so difficult to offer specific advice to you not knowing what has actually transpired during the biting incident...were the children playing with the dog? Feeding the dog? Did the dog suddenly go up and attack the child?  You are correct that this dog should not be trust for now.
I need to also question what level of discipline and training does your dog have.  there is so much that needs to be established prior to truly assessing this question and answering intelligently.  I would not totally give up on the dog if she is good with your family.  You may need assistance with retraining, discipline,communication, and establishing respect from your girl.  You would best be able to assess this or seek the assistance of a good local trainer or your vet.  Here is a website that will give you some insight into the roots of dog behavior, the possible causes of certain bad behavior, biting and training solutions, aggression in dogs (particularly food and protective), and your role as the leader.
http://www.uwsp.edu/psych/dog/dog.htm#cont
I believe  you will be able to locate some ideas from this website. As I mentioned, you have seen the circumstances and the behavior so you would be the best judge as to what issues are most important.  I would look into the specific problems but do not overlook the root behavior and also training or retraining basics.
I wish you the best.