Hedgehog - I am also the mother of a type 1 diabetic and you are doing the right thing. I honestly don't think that someone who hasn't had the experience of this condition as a parent can comprehend the importance of having plenty of medication onhand. Type 1 diabetes is hugely misunderstood.
Without insulin or the abilty to monitor how much insulin is required etc my child will die. Simple as that. Keeping a stock of insulin that will without question be used, isn't the same as keeping headache tablets etc that you might need someday. The thought of not having that medication that keeps your child alive hanging over you all the time is pretty stressful let me tell you, and caring for a child with type 1 diabetes is hard enough without people potentially messing up their prescription. I know many think it involves a couple of insulin injections a day and that's it, but honestly, that's the easy part. The constant need to be monitoring what the child's bg is, working out what they've eaten, how much to inject for it, what effect the slightest bit of exercise they are doing is having on their bg has to be in your head all the time. If you get it the slightest bit wrong you are at risk of them having a hypo and maybe dying. You live on edge all the time. There is no let up ever. 
We have had all sorts of trouble in the past with prescriptions being delayed or the chemist having trouble getting the insulin in stock etc and we absolutely need to have a good supply at home in readiness of this. We have also had events where snow has prevented stock getting through for example. Not to mention the fact that it becomes incredibly time consuming ordering repeat prescriptions and picking them up all the time.
There is nothing wrong with questioning both gps and pharmacists. They are humans and not infallible. They do make mistakes sometimes, and you are the expert on your child and how their condition affects them. You live it day in and day out, they don't. You will find many occasions when you have to stand up for your child when it comes to things like this. Do you have a good diabetic nurse and consultant? They are the ones who can help you the most with any problems you have regarding the gp etc.
I would suggest that if possible you do change the chemist that you visit. The relationship you have with them is very important. We had to change our one initially and now have one which understands my son and his condition well.
I am also very perplexed at the person claiming to be a Dr that mentions an insulin overdose. It's not something that is relevant to the thread in the slightest, and considering they claim to be a type 1 and a Dr it sounds like they don't have a good understanding of the condition. I find that very worrying and would ask them to kindly explain exactly what they meant?
As hedgehog said, a unit or so could be too much insulin depending on the bg beforehand what the child eats etc. Do you really think a parent of a diabetic wouldn't be aware of injecting too much insulin? The way you worded your post made it sound like it was a heroin!
As for saying there are advances being made all the time. We thought that when our son was diagnosed 18 years ago. Guess what? Nothing has changed. His medication etc is still all the same.
Type 1 diabetes is a huge money maker for the drug companies, and therefore I really can't see much changing anytime soon. The few things that I believe would help him live better aren't available on the nhs anyway as they won't fund them in this area.
Apologies for the rant, but I feel Hedgehog is getting a hard time and really doesn't deserve it. All this talk of her "stashing" medicines doesn't seem helpful. She isn't "stashing" it. She has it in her home to be used, and it will all be used, so I'm not understanding what the problem is?