I'm not sure whether you are saying hypos in the day happen before hypers at night or hypers at night first followed by hypos in the day?
If she is going so low in the day that this causes a liver dump response then the hormones released due to the low are counter regulatory to insulin and that might cause hypers in the night. I hope she isn't having such severe hypos that she is getting a full hormone response sending her high because that would be fairly dangerous and unpleasant.
If it's hypos first have a think about how to reduce them, maybe I:c ratios need adjusting to a count for running around and playing, treat quickly with a small amount of fast acting glucose, think about treating pre-emptively before she drops low.
If she is having hypers first, it could be correction doses are stacking to cause hypos later in the day, it could be that the basal dose is not high enough at night, but too high for her in the day. You might need to look at splitting the basal dose, or looking at a pump.