It sounds as if your DD is crying out for you to take some of the responsibility off her. This child led approach, where she decides everything, while it's happening and emotions are high, is exhausting for her and isn't going to do her any favours in the long run. There is a balance where you take their opinion into account but don't overwhelm them. Control how much responsibility she has - before you start, pony tail or pigtails - but don't give her open ended questions yet, she's too little. Don't even ask her if she's happy with her hair until you've reset the idea it's her job, just say "All done, let's go and do x fun thing now!" What looks to you like giving her control, is really piling on the responsibility.
You sound so unsure of yourself, even the back and forth at keeping her off school. You have made that decision, move on. There isn't enough hours in the day to spend this much time on a minor decision. Show her how freeing it is to make a decision and move on with your day - learn this yourself.
Try not to validate to her that a slightly imperfect hairstyle is a reason to cry and not get on with things, you should be the adult giving her a sense of perspective and showing that her hairstyle doesn't really matter. The first time she complained, I would have said "if I'm helping you, you do not talk to me like that," and walked away if she tried to make a drama out of it - life is too short. Being kind and polite is more important than the exact height of a pigtail, you need to show her this, it doesn't come naturally. Your job at this age is to move from the phase where you adjust her surroundings to suit her, mashing food etc, to showing her how to adjust to the world.
My DD is 11 and as they got older, the kids parented as if the world revolves around them have become more and more unpopular - can't lose a game, can't stand someone having something they don't have, bossing people around. If you find it tiring and hard work to be around your child, so will other children. It's no small gift to give her a wider sense of perspective and the social skills to think about other people.