I too have a strong willed/ spirited toddler and these two books have really helped us decrease the tantrums and battles:
Raising Your Spirited Child: A Guide for Parents Whose Child Is More Intense, Sensitive, Perceptive, Persistent, Energetic [Paperback]
Mary Sheedy Kurcinka (Author)
Setting Limits with Your Strong-Willed Child : Eliminating Conflict by Establishing Clear, Firm, and Respectful Boundaries by Robert J. Mac Kenzie
(Both books are on amazon)
Also, I have found that letting my daughter know what comes next helps and making things more fun for her. Also limit distractions. This limits the conflict for us. I do her hair while she washes her hands, if you park in the garage you might take her coat and put it on when you get out of the car at your destination just to get out of the house. The shoes! We had this problem too. We carried her to the car distracting her (singing, big hugs, she's flying etc and then get her in the car seat..now put the shoes on. There is no battle.) We had success with the shoes and coat so we now moved them to a bench in the (mudd room) garage now so she can put them on with her coat with out any distractions and now "races" to the car seat to be the "first one in".
As far as the the yelling at you, my daughter was yelling "get out of here" in the mornings. Nip it as soon as you can because it got worse for us at age 3 . We finally stopped it by making her apologize and then thanking her for her apology and then letting her know what she could say " You can say...Dad, can I have more time? , or Mom I want to do it. Then she usually says it in a softer tone and we respond in a soft calm tone.This seemed to help A LOT.
I fought with my daughter every morning to keep her clothes on. Finally we came up with the idea to have "Princess dresses" "Rock star dress" etc.( I just went to a consignment store a bought a whole bunch of basic cute girls dresses.) She knows she has to wear leggings under them when we go out but she keeps her clothes on now. I remind her about 5 mins before I put them on her but when we get home she gets to take the leggings off if she wants to.
Naps were a fight too and now we have "Nap Nap" dresses that she only gets to wear at Nap Time" they are just sleep jammie dresses I got at Osh Gosh.
One more idea I haven't tried yet is making pictures with Velcro on the wall or a board in order of what comes next. When she completes the tasks she gets to attach the photo. Then she can show the other parent the completed game. I have heard this works great.
Sorry I had such a lengthly response but I really wanted to help. We are going through this but we are seeing some great results and it is getting better with a lot of persistence on our part. I know it is easier said that done and harder with spirited children because they test ALL the time.
Hope all this helps. You'll get through this!
Updated
I just read Megan's answer. She is right on. Set your self up for success. Have the milk ready, etc. Have the next step ready to go to help make it happen with ease. A lot of our meltdowns happen during the time I am getting things together for her. Once you get one step ahead of her it helps.