Help me remember this movie that isn't Spirited Away
Here is a guess, it doesn't fit exactly - but hopefully the fuzziness is to blame for that.

I looked through all the old Ghibli works, but didn't find anything that seemed to match up. However, there was one show that some of the larger names from Ghibli worked on before Ghibli was created. This show was Chie The Brat or Jarinko Chie. This was back in 1981, but it could have taken a while to be translated and localised for English speakers - placing it roughly mid 80s.



Chie is a hardworker at home, but she's not without her brattiness - Flicking through the first few minutes of the show, she takes a cut of the family's earning and keeps it for herself:



She eventually leaves on an adventure after her school-life is disrupted by her relatives, who barge in and embarrass both the teacher and herself.



She then takes the money she has stored away and travels into the city. There she finds a woman she treats like her mother (whom she embraces occasionally) and rides rollercoasters, paddles boats, and other adventure-y things.



And as for the spirit/animal - there are some talking cats which maybe are what you remembered. The two cats are both from Chie's home village and have a large fight in a graveyard near the conclusion of the show.



Again, this only loosely fits the description you've offered - but it's the best I could find.