I don't know why the psych couldn't diagnose ADHD, but fwiw it sounds like perhaps the psych didn't administer any kind of behavioral survey, which is usually a key part of diagnosing ADHD (surveys are filled out by parents and teachers).
I also don't know anything about the WASI, but re the relative drop in scores between the WASI and the WISC - in general, I'd suspect that testing is less reliable in very young children. I don't say that just as a parent throwing something out there either, one of my dds was first tested at 5 years old, and has had IQ assessments twice since then. Her IQ scores dropped by 20 points from the first testing - and having several years worth of school behind us at this point, my gut feeling is the lower scores are, for her, the more accurate representation of her IQ. OTOH, you noted that it took months for your dd to get through the WISC testing - I would look at the results with a bit of a grain of salt there. Rather than worrying over which score is more accurate, I'd focus on figuring out if the relative dips you see in WISC subtest scores match up with any challenges you've seen at home or at school, as well as taking in what the psych's comments say and seeing how they fit (or don't fit) your dd. The follow-up with a developmental ped is a really good next step.
I'm curious if the psych who did your dd's recent testing followed up with any tests to help understand the relative dip in working memory and processing speed? As fwtxmom mentioned, these scores can be depressed in children with ADHD, but they can also be relatively low for other reasons. My ds12 (dysgraphic, developmental coordination disorder) has a relatively low processing speed and it impacts his life in a *huge* way - in his case, it's due to a neurological challenge that impacts fine motor coordination. When he had his first neuropsych eval and the psych noted the dip in processing speed she administered additional tests to rule out vision vs fine motor vs executive functioning etc.
FWIW you mentioned your dd accidentally hurting her brothers and bumping into things - you might want to have her vision checked - not just her eyesight (regular vision exam) but how well her eyes function together. My older dd had severe double vision up through 2nd grade that none of us ever realized she had simply because she was so used to it she thought it was normal! She also had a relatively low score in processing speed on the WISC, and always seemed to be bumping into and accidentally breaking anything and everything. Part of the reason I mentioned this is your note that your dd has challenges with following multistep directions. When our dd was young and before we knew about her vision challenges used to seem to have some incredible challenge with memory - she couldn't follow through on most single-step directions much less multiple-step directions - we really thought she must have some type of cognitive challenge. It was all somehow simply tied into her inability to see well and once her vision was corrected the issues with following directions disappeared (and much less accidental breakage occurred!). She was also mistakenly thought to be ADHD by many people (me included)... but she didn't fit an ADHD profile on behavioral surveys and she didn't exhibit the clumsiness and always-on-the-go fidgety behaviors at school - which is one hallmark that is required for an ADHD diagnosis here - the ADHD-like behaviors should be present in more than one situation (home & school).
Can you give us the subtest scores on processing speed on the WISC? That might help shed a little light on whether or not the low processing speed score is related to vision or fine motor (of course it could also be low simply due to ADHD).
Best wishes,
polarbear
