She has had previous IQ testing done before. The WISC-IV when she was 7 I think. Here are her scores:
Verbal Comprehension - 128
Perceptual Reasoning - 125
Working Memory - 126
Processing Speed - 106
Full Scale IQ - 128
FWIW my ds, 11, has a learning disability. His IQ scores have a discrepancy similar to your dds - her Verbal Comp and Perceptual Reasoning are higher than her Processing Speed. If you have a copy of the subtest results, take a look at those. Although my ds' Processing Speed average score on the WISC is around 110 or so, he had a subtest which is very very low, and that is related to his learning disability.
You also noted she has a hard time tying her shoes - that was another sign in our ds that we didn't recognize. His disability is tied to fine motor skills, and ultimately impacts the way he writes, how he organizes thoughts in order to write, etc. He has other things going on too, some of which sound similar to your dd.
The one thing that is different - our ds has a wide range of scores on his achievement tests - some are very high, some are average, some are very low. The variation in scores makes sense when we look closely at what specific skill is being tested, what kind of queue (visual, auditory et) he's given for each question, and what type of response is required (oral response vs handwritten). Timed vs untimed also makes a difference in his case.
We went to a private neuropsychologist for our ds' diagnosis - sometimes insurance will pay for the assessment, in our case it was covered because our pediatrician referred our ds for anxiety. Our ds has also been tested through our school system but we had much better luck getting in depth information and having questions answered with private evals.
Best wishes,
Kath
