Yes, I don't really remember a terrible two phase....it's the challenging 3 phase that was rough. No easy antidote but it does help to remember that the stubbornness that you see, now, could actually be a benefit into those preteen/teen years. I really miss those young ages but I do love the age of my kids too!
Just do your best to personally use the mantra..."respond - don't react". When she's yelling or defiant, don't yell back (your two older ones are watching you constantly). I learned from my dad that, the more heated the situation, the softer and slower I speak. I use this in a classroom situation all the time or when I am speaking w/ a roomful of noisy kids. It's a good tool to master. Positive reinforcement can go far but use it when you are NOT in the heat of the moment and use it often. (i.e."Wow, I noticed that you were: sharing nicely...using your manners...speaking nicely... you were putting your toys away promptly...., then "Thank you!") Give options.... "you can do this or that"....however, my son, used to come up with option #3 all the time so, if it works in your schedule, consider it.
She should be disciplined and have "time outs" and your older ones expect her to get it, too, so, there will be those moments. In order for them to be effective, find her "achilles heel".... what makes her tick. Maybe if she is not acting nicely, her favorite "lovey, stuffed animal, blanket" gets grounded for an hour! (For my daughter, this was a killer! Once she hit 6 years, the writing assignments were very effective.) Make sure she knows exactly why she is grounded, then administer the punishment. Lastly, end the punishment my saying, "Why were you grounded?" and let her tell you. If she can successfully tell you and say I'm sorry to the offended person, then say, "Your grounding is over. Now you can be good." Don't keep bringing up the event.
I never tolerated bad behavior in stores. When my children were 3 years old and 6 years old, they witnessed me leave all my stuff in a cart, in the middle of the aisle at Target (most of the stuff I was buying was for them - that helped!) and walk out the store. Sure it was inconvenient for me but .... it only took one time! They were given a couple fair warnings, then...without yelling (just a little drama!) I took my oldest's hand and the youngest was carried out, under my arm like a sack of potatoes. To this day, they remember it. However, they still love going shopping with me and on a good shopping trip, a hot wheel car, pack of gum or some trinkety item gets purchased at the end of the trip.
One last thing, kids know that it is the Holiday season and they can sense our tension, tiredness and stress. Just try to do your best to put aside a little quiet time with the kids and read a book or play a game of UNO or something. (I'll heed that advise too, just as soon as I'm done decking my halls! Best of luck to you.