Strong willed children are sometimes a challange when it comes to things like potty training. It means regaining some control while at the same time allowing the child to have some autonomy. It is also interesting that the "apple usually does not fall far from the tree." Hmm, I wonder where I could find a family full of strong willed children. :-) Parents who raise their children in an environment where they gain a high degree of trust, become more self assured as they move into the autonomy of the second year, They then seek more control over everything. Here are a few steps I would suggest.
1. Cut down on how often you check to see if she needs to go to the bathroom.
2. When you do ask, change the question from: Do you need to go potty? Which allows a no for an answer, to: Do you want to go right now or do you want to go in three minutes? 90% of children will want to wait, especially if they like being in charge. Once they made their choice then you are merely enforcing their choice.
3. Have a book or two that are only for in the bathroom.
4. After the child goes in the toilet the party is not over. Children need to spend more time to fully take care of business. Have them stay until the story is over, the timer goes off, etc. so that they give their bodies a chance to relax from the tensing it does after going a little bit. It is interesting that a large number of children will actually mess their pants within 20 minutes of peeing in the toilet because their bodily functions are not in sync.
5. Use a reward for being successful for a whole day for a child that is almost three years old. They are old enough to understand what you are asking. When accidents happen, say "that's okay we can try again tomorrow." If you think a full day is too long a time then go in half days.
6. Involve the child in clean up but don't make it too special.