Ask your nurse, they won't mind explaining it all. I assume it's something to do with the levemir not lasting 24hours, but in any case don't worry too much about the figures right now, as long as it is improving that's the main thing. You can't expect perfect control right away, but the day 2 readings are much lower so that's a good improvement already!
Hopefully the nurse will explain carb counting and correction doses to you and your daughter soon, I think they don't go into too much detail at the start, or else it would be information overload!