Read: 'Raising your Spirited Child'. 15% of all of children are smarter than we are - which is why they cannot be "reasoned" with and are called "spirited". Spirited, smart children need tactically smart parents. This book will save your life. You are fighting with someone who knows exactly what her rights are and where your power ends (your power ends when you begin to fight). Read the book NOW! You will not regret this one Ann.
Smart girls are always up for a good fight. What she needs is an internal (intellectual) reason to potty train rather than an external reason: Your Anger or Her Ability to stay in her day-care.
Get her the books: 'Once upon a potty' and 'Everybody Poops'. Stop arguing with her and fighting... it is just making things worse for everyone involved.
In the end, what you really want is a cooperative and fun relationship with your daughter. The promise of Raising your Spirited Child is just this. You will go back to loving each other ALL the time - not just when she is doing everything right.
The potty training will take care of itself over time, however, you won't know how long it will take to heal the wounds of all the fighting you have been through thus far. I'm afraid you will have to let go of your timelines Ann. Kids potty train on their schedule, not yours.