Why is my grandmother taking double doses of her insulin and medication every day?

Take the bag and let her call the police.

She can die from too much insulin and then you will be dealing with the police with a dead body to answer for.

Where are her children? Someone needs to intervene if you are worried about dealing with the police about taking her medicine bag so she can not kill herself.

I would start by hiding the meds once you put them out for her each morning. Don't let her know you've done that or let her see you do it. It may be that "out of sight, out of mind" will be enough to keep her from double dosing. That is a short term suggestion. Long term you need to get this situation sorted more permanently because she's unlikely to give up control of her medicine bag, which to her represents her independence. Both her forgetting she's already taken her daily meds and her argumentative reaction point to short-term memory loss and the beginnings of dementia which will need to be dealt with soon. Especially if she has diabetes she needs over oversight of her meds and food intake to keep things under control. I wish I had better suggestions for you but all I can really do is warn you that things aren't going to get better with this and you need to be pro-active including mentioning this situation to her doctor.

This appears to be about who is holding the medicine bag. You or your grandmother. But not both.

How come she accepts your support to set out her morning meds, but then undertakes the same routine herself in the afternoons and declines to hand control of The Bag to you?

Is she falling asleep after lunch, waking to think it is morning, and going through her habitual routine, something like that?

You need to get to the bottom of what's going on when she takes the second/over dose.

And you need to be firm about Safe Handling and Administration of Medications. If you were employed in this role, you would have more regulations to follow than you can shake a stick at. So go about it in a business-like way and tell your grandmother you're either doing it properly or you won't do it at all.

Agree with Mysteryshopper...short-term memory loss. It's not going to improve or stay the same. Is she responsible for feeding herself as well? She may not remember what she is eating or how much (or if she's eating at all). The thing about memory loss and personality changes is that even if you set up all kinds of workarounds or reminders, her logic and reason are declining and she may not see the need to "cooperate" with the system in place.

Are you or GM testing her blood sugar during the day? Is that how you know it has dropped too low?
Isnt she running out of meds before it’s time to refill? What then?
i can see why you are concerned. Who is her medical POA? Time to take action. Call her doctor tomorrow. Don’t let this continue without professional advice.

I don't know why she's doing this - other than she's just plain forgetting that she already took the medication.  However, an endocrinologist once told me that too low of blood sugar can kill a person so what is happening is highly dangerous.    Sounds like she can't self-administer medications anymore and she may need to be relieved of that job.  I have been through this.  I took and hid the meds against LO's wishes to avoid her mismanaging them.