I'm sorry you are both having a tough time of it. First, your DN should ask her to check her basal insulin by eating a carbohydrate-free meal, and not dose short-acting, to check the blood sugars holds a straight line. You can do this for lunch one day, and a few days later for dinner. Second, I recommend you keep a detailed diary of blood sugar from a finger prick (which may be different to the Libre - your DN would have said never dose insulin on a Libre reading) waking, bedtime, before meals and 5 hours after, and a record of food eaten, and insulin given over 4 to 5 days. This will help the consultants get to to the bottom of what's happening in terms of dosing.
Of course, other tests, as suggested in the posts above, for the collapsing pre-insulin, and other medical issues, need to be followed up on.
The Bubble is a competitor to the Miao Miao, which you should look into as well, but both have alarms which are life-changing and great. Also phone apps such as X-Drip and Glimp to connect to the Miao Miao or Bubble, you can use to calibrate your finger pricks. Don't be afraid of setting night alarms to check blood sugar if you see a pattern, for example, always going low at 2 am. I set one four hours after taking my bedtime night basal when I started insulin, just to get a picture of what was happening when the basal started working (it starts 4 hours after the injection for Levemir) before I had a Miao Maio.
I really hope you get to the bottom of what is happening soon.
I recommend this online course:
https://www.bertieonline.org.uk/