Yes, even children, have hormones. It is not age based, I believe, and per our Pediatrician. But perhaps it is not "hormones" in the sense of women...but they are girls after all, and their body is wired differently, just physiologically. And they are growing all the time. The endocrine system is so complex...
Here's some links:
http://www.parenting.com/article/Toddler/Behavior/Ask-Dr....
http://www.parents.com/preschoolers/socializing/social-gr...
It's good you have observed and recorded her behavior. The rash though... it sounds like "hives" of some kind...this kind of thing DOES disappear quickly and/or pops up in different locations. It's an allergy of some kind... to either something topical or something ingested. Both my kids have had hives and I took them to the Doctor, and this was what they told me. Do you think the rash is always on her back because maybe as she's sleeping on her back it sweats?
My girl, I swear, gets rather "PMS'y" too... sometimes. The Doc says that they hear this all the time from Moms. But again, I don't know if a study has been done on it.
Or, there are other reasons for her behavior.... it could be anything, since it sounds only since she has been attending Preschool?
There is a book called- "Your Three-Year-Old: Friend or Enemy (Paperback)
by Louise Bates Ames (Author), Frances L. Ilg (Author)
You can get it on Amazon.com I have found these book quite illuminating. It's an easy read.
Perhaps check with your Pediatrician.... there must be some REASON for her meltdowns... or hives. And maybe it's related or not...
All the best,
Susan