In any case [/b] is known as a discourse marker. That means that it is supposed to add information or arguments to what has already been said.
I think the easy way to see if "in any case" fits the context is to replace is with "besides".
It doesn't seem to click with "besides, either. Your second sentence doesn't really add to the information but answers the question why you think she wasn't on the train. I would use a different discourse marker and say " I am afraid I think she didn't have enough money to buy a ticket.
"