It would seem to me that one of two things are happening here. No one gets a 600 mg/dL reading without falling off the wagon. Type 1s that even edge up beyond 200 quickly find out what's wrong and tighten their regimen up. To let it get to 600 mg/dL...needs some close scrutiny.
Second, to get to 600 mg/dL, either she's not taking her basal and bolus insulins correctly...or the insulins are crap, compromised, out of date, or possibly useless. There is no way to test the insulins...so I suggest after she gets out of the hospital that all insulin be replaced...to rule that out as a factor if it's not her diet.
For a Type 1, diet is very important because of the intense affect it has on blood sugars. They not only need to have their basal insulin dialed in...but must know, absolutely, how to cover their meals with a bolus injection. A Type 1 getting a reading of 600 mg/dL and landing in the hospital...I'm going to have to assume they either have no knowledge of how to test before and after meals...or whatever doctor prescribed her insulin amounts doesn't know WTF they're doing. Or both!
I'm curious as to what information she'll come home with from the hospital doctors in regards to this setback.
Doctors, in my opinion, are a waste of time other than being used to write a script and order labs. If her doctor isn't a help...get another doctor. If she lives in some podunk town where doctors are at a premium then go to another town. What's important here, above all else, is results.
When should she test? I suggest that she take a fasting blood glucose test in the morning when she rises. That will give her a ball park figure of how her basal insulin is working. Test before a meal and adjust the bolus insulin accordingly to the amount of carbohydrates in her meal. That ratio, the amount of insulin units per carbohydrate she should already have figured out. Since she's in the hospital with diabetic ketoacidosis...I'm a little suspect to how that's being handled.
As well as diabetes message boards and forums there's a glut of information on the internet about how to get this thing under control. But information is just that...information. Without practical application all the information there is...does nothing.