Ours took about 1-2 weeks, but I don't know what would be typical. I've read reports here ranging up to many months to get testing results, but IIRC those were from testing by a school psychologist.
I think that no matter what's typical, I would be frustrated too. I think what's most likely happened is that your tester put your report on the back burner, and is most likely working on it now. I would be politely persistent, remind her of her prior promises and the possible need for further testing, and ask her for an appointment at least 4 days in advance of starting back to school. There's no reason she can't get a report done in several days, after letting it go for so long.
With regard to the follow-up testing, it doesn't seem like you will get the results by the first day of school no matter what you do, even if you go elsewhere for further testing. If you commit to further testing with this psychologist you may want to get her to commit to a date when the results will be ready, stressing that time is of the essence because school will already be underway.
