"Then my sister insisted."
Translation:Luego mi hermana insistió.
I ran into the same problem.
This post claims that luego means "later on" and entonces means "therefore": https://spanish.stackexchange.com/questions/12196/difference-between-luego-and-entonces
It seems to me that both could be valid in this context, but I'm just trying to learn the language and I could be wrong.