K.D.
My daughter (also the youngest, only 19 mos.) is very willful too. To the point that she has to do everything herself even if she can't do it -- like peeling an orange. With her (and with my older son) when they started this temper-tantrum phase, at home I would just let them have a temper-tantrum wherever they were and say to them "Let me know when you are done and we can discuss it." Then I usually walk away or go back to what I was doing and ignore them. On a particularly bad day, I even let my son do it at the grocery store (ahh, the horror -- you can imagine the stares I got, but we were completely out of food so just leaving wasn't an option).
Squawking and yelling like this is a cry for attention, so the best way to correct this behavior is to resolutely ignore the child when she is behaving badly AND pay close attention to her when she is behaving correctly. It's hard with more kids and your youngest may just be trying to get her share of mommy time -- even if all she gets is the time you are carrying her to her crib. Get your older kids in on the action too -- because attention from them also reinforces both bad and good behavior.