This calls for a family meeting! Have a round table discussion about what responsibilities your teen and other family members are expected to have. The expectation would be that everybody fulfills those responsibilities so that the family's life can go on smoothly.
Since your 14-year-old is opposed to positive reinforcement (reward system), tell her what consequences there will be for not being responsible. For teens, withholding privileges works like a charm! You can also agree that if all chores are done without complaining and delays every single day of a month, there will be a reward, like a trip to the movies, etc.