Sometimes a more persuasive tack is to say 'Let's clear away a good few of these toys now so the room will be ready for X activity' , so you are doing it together to some extent instead of standing over her giving her an order that entails her either giving in or fighting against you. Getting down to the floor to get started together on something you want her to do can work better than looming over her.
Doing something boring and unappealing in turns makes a task seem more fun -- alternating putting blocks back in their box together for instance, or DD putting away the blue ones/rectangular ones, etc. while you do the red ones, with a race to see who can get most of the stragglers; high fives and ott enthusiasm plus a smile of encouragement along the way can help reinforce the message that co-operation can be fun and rewarding. Catching her being co-operative and complimenting that can make her very pleased with herself.
Three is a tricky age because they are so much more verbal and have a lot more stamina and reasoning ability but still so very immature in ego terms. They need a cheerleader/companion by their sides though.
Allowing choices between reasonable alternatives that you have pre-chosen can help boost self confidence and can also reduce the amount of fight she has in other areas. Helping her to develop positive autonomy as opposed to training her to do what she is told should be your aim here. Make boring and necessary tasks fun, reduce the direct orders, chat plenty about her thoughts and fancies what she likes and anjoys, finds pretty, whether she would like to be a bird and what that might be like, etc., help her to develop competence in self care such as dressing (allow lots of time and help a little without seeming impatient), hair care, washing herself in the bath (if she has one every day it doesn't matter if she misses behind her ears), encouraging wiping herself after a poo if she doesn't already do this, maybe with you checking afterwards. A 3 year old can be helped to see herself as an important part of a team if she gets to help set the table or clear away or assist in putting her clean clothes back in drawers, with you being patient and positive working alongside her.
There are lots of ways to reduce the power struggle element and still get what you want done. Try to see yourself as a teacher/coach. Focus on engaging her positively in the process and not on the results of her efforts for a few years.