@shivles I second the advice to check with her DSN. I would ask if it was sensible to try 1 and a half units of basal, split in the way they advise. You could, if you think it's appropriate, also ask their reasons for dropping her basal down from 2 units to 1 unit.
If you compare the chart above with the charts you got when she was on 2 units of basal, you may get more clues as to what's going on. We can only guess, and none of us are medical experts. It does seem like it might be the basal, but I would discuss with her team.
@tim2000s I believe artificial sweeteners aren't recommended for children under 3 and aren't permitted to be added to foods for them.
That aside, I quite understand why you don't want to do a basal test, Shivles. I wouldn't think its right for such a young child, and I wouldn't do it to my son if he was diabetic. You should be able to work out appropriate doses without doing a basal test - with the help of your team and your thorough records