To me, the "caregiver" situation really does sound like a close relative who helped with Jayme because of her parents' work schedules. I live in a rural, poor area with a lot of factory workers, and it is very common for grandparents or aunts/uncles or even family friends to be the one taking care of children while the parents are working. (In fact, that was true for me growing up.)
Edited to add: it seems to be the preferred method, especially since childcare itself can be costly and people have to work and often live paycheck to paycheck.
Switching schools really could have just been a matter of convenience, especially if the person taking care of her had their own children at the other school or were older and it was simply more convenient for them to have the school closer to where they lived.