The one I struggle with most is leaving enough time to get dressed. DS is 3.4 now and I still find it hard on non-nursery days, I leave it until the last minute and then panic, and yes, shouting, bribing and arm forcing happen. (Although he's big enough and strong enough that arm forcing is difficult and more likely to hurt him - another good reason to try and break the cycle!)
When you're running late, they seem to pick up on your stress and react more to it, you're more likely to then panic and react in a way which makes them kick back and dig their heels in more, getting stressed because you're thinking "This would take 5 minutes if she would just co-operate!!" rather than remembering she's two and so unlikely to always co-operate, having the patience and time to react in a playful or other diffusing way which although it might take 10-15 minutes, is still quicker than getting into an argument about it.
I sympathise as it's really hard dealing with mornings on your own, especially if you've had interrupted sleep during the night or other broken sleep patterns (I often fall asleep with DS and then wake up and am up until really late) - patience is often hard to come by. The calmest mornings were when I got up before DS but this isn't always possible if you have an early waker.
If you don't want to use TV, I still recommend having some kind of fixed point as a marker for leaving - perhaps it would be worth setting an egg timer, or if you have to leave at e.g. 8.30, get a digital clock and cover up the last digit so that she knows when it is showing an 8 and a 3 that it is time to go. Warnings of "5 minutes" are really meaningless to them. It helps to explain it in terms of events, so "Mummy is just going to go to the toilet, and then it is time to get dressed." or "You can put that marble down the track three more times, and then we have to get dressed."
If she's shouting at other times, not due to anger but just due to impatience, habit, or perhaps mild irritation that you're not jumping immediately to her every whim
- again, try to squash the urge to shout back yourself, and do a variation on the not understanding thing, I tend to say "I don't like being shouted at. It hurts my ears. Can you speak nicely, please?" perhaps progressing to being a little more firm if this is not working. "I don't like being shouted at. I will listen to you when you can speak nicely." and then do ignore, until she at least makes an effort to tone it down. I use it if DS is overly whining as well, I say "I can't hear what you're saying very well, can you speak nicely?" even if I know what he wants. I have resorted to saying "If you want to make that noise, you're going to have to go and do it in another room because I don't like it." on occasion as well. I am always careful to tell him "It is okay to be upset, DS, if you want to cry, that's fine, but please stop making that wailing/screeching noise." because I don't want him to feel I am telling him to stop being sad/expressing his emotions, I would just like him to do it in a less painful way! DP is prone to telling him "stop crying" and I hate this, it's one of my pet hates with children.
Also - don't fall into the trap of feeling like you have to reward every time she does not shout, so if she is shouting "I WANT SWEETIES" repeatedly and you don't want to give them to her, you still ask her to ask nicely, but then don't feel "Oh no, she's just done something for me and now I have to give her what she wants because she's been good!" you can still give a calm "No, it's nearly time for dinner." and then deal with the fallout appropriately - ignore, cuddle, offer alternatives, give a delayed "yes" e.g. "You can have sweeties tomorrow/you can have a yoghurt after dinner." I think though that in the interests of consistency and showing that we don't like shouting for any reason it's best to try and avoid responding to the "I WANT SWEETS, I WANT THEM NOW" type tactics with a curt "No! You're not having anything!" - asking her to ask you nicely shows her that you're listening and taking her request seriously, even if you say no. (Hope that makes sense...)