I would say that the results you are getting are not worryingly bad. It is very hard to control someone else's diabetes when you cannot predict whether she is going to be flying round the playground at lunchtime or in the library reading, for instance. Either way she is going to need different amounts of insulin for her lunch and other meals.
You have already studied the peak times for her insulins, and you can use that for a fair guess at which one is to blame. A pretty good rule of thumb is that if her levels are mostly low and needing correcting (which can, of course, cause corresponding highs), then the fault is probably in the long acting insulin. Also if she has hypos in the early hours of the morning long after her short acting insulin is out of commission, that is going to be the basal as well... having said that, sometimes I am sure that too much short acting contributes to my night time hypos, but maybe we'd best not go there... too weird! :?
If her hypos - in my book, anything under 4, but that is entirely personal and different for us all - are happening now and then between meals, but not regularly then it is likely to be the short acting that's the problem. Whatever you do, do not change both at once or you will never find out which one it is. (Now I'm picturing you thinking 'Does she think I'm stupid?' because that is so obvious.)
I am surprised that you have not been given any education about insulin/carb ratios. The DAFNE (Dose Adjustment for Normal Eating) courses are being rolled out across the country, at least they were a while back, I don't know if 'cuts' have made them think it's cheaper not to educate us :shock: , but someone can tell us if they are still going and becoming more available. I don't know whether they are using the system for children yet: I believe there was some idea that it wasn't a good idea, but that will just start me off on another rant. It is essential to understand how to work out those ratios and how to adjust them according to your daughter's exercise patterns - or unpatterns because she is little and exercising to order I don't suppose is possible.
The one variable that is impossible to predict is emotion which can mess things up royally. It so often happens that the exact same routine can be followed one day after another with completely different results because one day there was adrenalin in the system and the next there wasn't. Or brewing for a cold or other infection messes things up too.
I have often likened diabetes control to being on a seesaw, trying to keep it balanced with both ends off the ground. One end only has to sneeze to upset the balance because it is so fine, and that can represent the odd sneaked mars bar that didn't get injected for, or the mad run around the block racing her friends. But the variable you can't control is the crazy guy standing in the middle of the seesaw jumping unpredictably from one side to the other bringing the thing crashing down without warning. That guy is called emotion and bugs, and just has to be dealt with after the event.
I learnt more in the five days of DAFNE course than I had in thirty years of trying to manage the thing without any scientific knowledge of how to work it out. I can only imagine how much harder that must be doing it third party for someone little. The course has allowed me to predict the crazy guy better and to keep both ends of the seesaw off the ground much of the time. You have looked up the online course, but it's worth seeing if the pair of you could attend a DAFNE course if they do them for children. It would give you so much more confidence and knowledge.
Everyone has said that you will never get it perfect and they are right. If you expect perfection you will always be disappointed and the targets you have set yourself are very tight. Don't worry if they don't work out all the time, it's not the end of the world and I know we all like to stay stable and it's best if we can, but the safety marker really is the HbA1c, and if that can stay reasonable then the long term outlook is not a worry.
Good luck.
