Is she eating rice? Because it plays havoc with blood sugar levels. Try and avoid rice, at least until you have the insulin regimen sorted out. If you eat eggs, they are a good source of calories, very nutritious, and good for blood sugar. Nuts are good for snacks.
I agree that you need to ensure that all the carbs are being covered before changing the basal dosage (Lantus). Also remember that once blood glucose gets up to the 300's, we become more insulin resistant. The circulating insulin has a reduced effect. Large amounts of it are required to get such high blood glucose down again, and all the dosage calculations go out the window ...

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As far as dosage calculation guidelines go, they only really apply to insulin sensitive adults. All the hormonal activity in children changes things, and you just have to use a trial-and-error approach. It means that you need to ensure that all the carbs are being covered, youe have to do a lot of testing, and Lantus dosages are titrated to levels that give the best results.