It's so hard when you are tired, I shout too and I hate it. I don't seem to notice I've slipped into the shouty voice until I'm doing it.
Sounds like others have had really good advice :) Another thing to try is to acknowledge that you are shouting, and try not to blame her for it. So if you realise you are shouting try to stop, count to ten and say "Sorry I was shouting. I will ask you nicely." and then try REALLY HARD to keep your voice level and repeat your request. If she's upset, ask if she needs a cuddle - sometimes you both need one!
Similarly if she ever says anything like "Don't shout at me, mummy!" really suppress the urge to say "Just do X then!!" and again, say sorry, count to ten if you need to, repeat what you want to say calmly, cuddle.
Always apologise after any shouting (when you've both calmed down) and remember to thank her if she is helpful/quick at getting dressed/whatever, even if it's been after a lot of messing around, verbalise feelings "We both got cross" and ask her how she felt, and tell her "It isn't nice to shout, is it, mummy will try to talk nicely." When she agrees, ask her if she can try to help/listen/get dressed (whatever the issue was). It will probably take a few times before she will respond to this positively but once she realises you are making an effort and listening to her, then she will, too.
When she is shouting at you, think about how it makes you feel - for me it makes me feel irritable and like "Well, no, I don't want to do things for someone who is shouting at me!" if you can try to keep hold of this it might help you when she is kicking off in relation to you shouting, because it probably makes her feel like this, too! If she is shouting at you use a positive phrase "DD can you speak nicely please?" rather than "Stop shouting at me, DD" - this isn't as important as the other things but it does help.
Also try to keep on top of your own sleep and eating if at all possible. It's so easy to forget to look after yourself when you have little ones - and I know the sleep thing is pretty impossible when you have a baby as well. If you and DH can agree on a plan where you both relieve each other if the other is getting stressed that can help a lot - DP used to instruct me to go for naps when DS's sleep was bad
I agree you need to get him on board with bedtimes etc too - his shirts can wait until she is in bed but she needs a set bedtime so she's not overtired.
Good luck! :) I hope things improve for you. And as BuckBuck says try not to take it to heart - think of each day as a new canvas, a fresh start and don't dwell on whether you feel you've "failed" previously, because you can always start again.