I had/have this problem with my DD who is also three, getting ready for nursery in the mornings. It actually goes in fits and starts, and tends to be worse when her little brother is teething/playing up - like she's competiting for attention as she is otherwise pretty well behaved.
During these phases I resort to making her get dressed before she has breakfast. This normally helps as DD has a healthy appetite and loves her porridge so it is an excellent carrot to get her going. She also HATES the idea that her teachers will disapprove of her because she is late, so that is often a tactic I use. We don't have issues with WHAT she wants to wear, just her various avoidance tactics on getting dressed full stop (including just running away laughing - annoying, non?).
I can only echo what just about everyone else has said - at this age, it's important to be consistent, but you will risk coming across as too harsh if you just expect a child of 3 (or any child for that matter) to just bend to your will.
Ask yourself this question - when she's 16 years old, and god forbid, ends up in a tricky peer pressure situation - would you want her to maintain some of this "I am my own person with my own ideas" spirit, or be the person who just does what she's told...
I'm not saying that's a green light to let her run wild or have her own way all the time - children THRIVE on boundaries, but distraction methods, bribery (emotional rewards over material ones) and illustrating consequences that will matter to them, are definitely the best way to go.
Also, I find that if I'm getting too stressed, I pause, then try my best to turn the situation into humour, because 3 year olds love nothing better than a good giggle.
E.g. DD will NOT get dressed and is running around house with no clothes on. I start pretending to be very proper person with proper person voice on but times 100 so it's ridiculous, saying "What on EARTH is going to happen if you go to Nursury in the nip?" You will get a "frosty bottom, an ice cube for a nose etc etc" until I get her laughing and on side and then just in a better mood, not so much seeing me as the enemy anymore, and then make a game of putting on her clothes (she responds well to idea that pants can be go faster pants etc).
I know this can be tough when you are knackered and stressed, but is is so much LESS stressful in the long run than locking horns with them every morning.
Good luck