I had a dog who became diabetic at 14 months old, and lived to be 11.5 years old- thousands of insulin injections over that span- and it does get easier! There were times when my dog would seemingly randomly decide that she wasn't on board with getting the insulin, and slink off to hide when she saw us getting the stuff ready, and I eventually discovered that some areas to inject evoked less reaction than others, so I tried to stick with them. Her evasive behavior was worse if someone was nervous/reluctant to give the shot, which made them more nervous, which made her more nervous, which made her tense and her skin tight, which seemed to make the shot more painful, etc... so relax! Easier said than done, I know
. I always gave a treat after the injection, and at times when she seemed reluctant, I would often give an additional treat before, just for coming over when she knew the shot was going to happen. You might also try a longer lasting treat, like a smear of peanut butter on a plate (or even his nose), as a distraction. I also had good success with "practicing" the injection technique with her as a trained behavior, then rewarding heavily for good behavior- for this I would call her over, have her sit, tent her skin, then not give the injection, but reward after as if I had. This seemed to help when she was at her most anxious, as sometimes nothing happened and she still got a great reward.
I would also look at factors involved with the actual injection process itself. Make sure your needles are as "fine"/small gauge as possible. If you are using u-100 insulin, there are needles as fine as 31 gauge. Not sure about for u-40 insulin. Make sure you are inserting the needle far enough to inject subcutaneously and not intradermally (within the layers of the skin). I always tried to warm the insulin in the syringe briefly in my hand before giving it. Make sure you are using a new needle each time, as they get dull quickly. Different injection sites may be more or less comfortable for a given dog... for my dog, the area right behind her shoulders was always the most sensitive (sometimes her skin would twitch so hard it would pull the syringe out of my hand!), followed by the skin further back by her flanks, and the scruff of her neck seemed least sensitive. The area on her flanks was at one point not very sensitive, but as she became a bit chubby and the skin grew more taut, she reacted more strongly. Your vet can advise you on other possible injection sites to try if you think that is the problem- I wouldn't change without talking to them first, as sometimes the location of the injection can affect the absorption of the insulin. It certainly can't hurt to schedule your next vet visit for a time of day when insulin is due, so that your vet can watch you give an injection.
My guess would be that he is more tense/nervous in general at the vets, so is less reactive to the injections there. They may also be injecting more smoothly just due to experience and lack of "this is my dog" nerves, which could make the injection more comfortable. Finally, there are going to be occasional injections which, for whatever reason, are just more painful than usual, and if you're giving the injection 98% of the time, you are more likely going to see it than the vet who gives it 2% of the time. You can't control that, so just say "Sorry!", give your dog an extra treat and pat on the head, and try again in a different spot. Not your fault, and treating your diabetic dog, even if it occasionally results in a brief moment of discomfort, is exponentially better for him than not treating him.
On a slightly unrelated note- I saw that you mentioned in another thread a concern about vet costs, and wanted to suggest talking to your vet about home glucose testing, if they haven't already mentioned it. It won't eliminate the need for vet visits, but you may not have to go as often for a simple glucose check or curve. Plus, stress can have an affect on the BG, so you may get more accurate readings by testing at home vs at the vet if your dog is nervous. My dog didn't mind home BG testing at all, despite her sometimes aversion to insulin injections.