Wow! Madonna's gained my respect if the "one outfit" rule is true!
When my son was 8-9, he decided that cleaning his room was "too hard". I made it much easier..........by eliminating anything and everything that was left on the floor after he said he had finished the job. I had told him the rules before hand...he chose not to do a good job, by not putting things in their buckets and bins.(I organized his room to be easy to manage, he was choosing to make it a big deal~Drama King!) So I simple got a large trash bag and started pitching in everything! Toys,clothes, cars, Batman stuff, Ninja Turtles and all the accessories, and legos.(I think they're just as bad as a million Barbie Shoes!!!) He was in shock that I followed through with it. I was serious, as I worked hard to provide a roof over our heads and food to eat, etc....his part in the family was to help maintain the house and his things, too. The trash bag belonged to me for 1-2 weeks. I think it was at this time, he discovered "goosebump" books. He then was rewarded with a new book each week if his grades and room were kept up! It worked.
Your daughter has things she values, therefore you have leverage. If she refuses to feed the cat, then give him to another family. That will send a clear message. Can you talk to Dad, and have him reinforce the rules for your daughter? I think rules should be mobile, as in "they go with the child", not the house they are at! Again, good luck, as I have been there.
A P.S. To all Moms of children that lose their coats and jackets~ 'tis the season! After my son lost a Starter jacket, and many other jackets, year after year. Each time he'd end up with a coat from Goodwill. What ever was left on the rack, in his size was the coat he'd have the rest of the winter. That cured that problem!!!!