Since when he sugars are low, she is likely eating something sweet or drinking juice, then her sugars rebound into high numbers. It is imperative she sees her Endo and brings them her glucose meter or glucose log to discuss medication adjustments.
This is more likely related to her medication, but, of course, it could be her eating pattern also.
First: Is she taking any medications for diabetes? The most common reason for waking up in the middle of the night or early morning is TOO much basal insulin (long lasting insulin like Lantus / Toujeo / Levemir / Tresiba / etc).
For diabetic patients, it is important to first get them stable through the night. This means checking a sugar BEFORE BED and then when waking in AM. The goal is to keep it steady overnight (i.e.: bedtime sugar of 150 to AM sugar of 150).
I personally do not like people going to bed hyperglycemic and drifting down ~100 points overnight (ie sugar of 200 to 100). This is because should we go to bed one night with a sugar of ~150 it may drift down 100 points to ~50, a low.
In short, take a close look at the insulins or medications on board and make sure we have not given too much long-lasting basal insulin.
The elevated sugars at noon are likely related to not enough insulin (or medication) given at breakfast to cover for the sugar / carbohydrate / glucose influx with breakfast.
I hope this gives you some guidance and feel free to post another message should you continue to run into issues!