@askun
I was thinking it was more along the lines of a legal prostitute, working at a
brothel
Being a traveling prostitute, just doesn't feel right to me. Dragging a kid to a strangers house then locking them up in a box outside?.... Honestly, I think if her customers knew about the kid, they wouldn't allow her to be kept in the box (for better or worse). And I don't see how she could drag her kid around with her without them noticing.
If she worked at a prostitute house, or at least had some form of advance notice, she could hide her daughter before they visit her.
Your explanation for her memory works well, I guess... Seems kind of weird though. Honestly, her morals, knowledge, and decisions making skills all seem like that of the kid before the "awakening". I don't see what she gets out of the "isekai" bit at all, except maybe a love for learning.
Thanks @Memnon for sparing me from having to add "house of prostitutes" to my google search history/personalized search results/personalized ads