Hi, welcome to the ehealth forum and I am glad to help you.
You seem concerned by the problems in controlling blood sugar as you suffer from insulin dependent diabetes.
In type 1 diabetes, iatrogenic hypoglycemia is more appropriately viewed as the result of the interplay of insulin excess and compromised glucose counterregulation rather than an absolute or relative insulin excess alone. Your problem seems to be the same only. You need consultation with your doctor for the titration of your insulin dose in tandem with regular blood sugar charting at various times during the day for which a doctor might like to admit you and monitor your blood sugar levels especially the early morning levels when you are facing the problems.
Hope this helps. Take care.
Note: This post is not to emphasise final diagnosis as the same cannot be made online and is aimed just to provide medical information and no treatment suggested above be taken without face to face consultation with health care professional.