You are certainly not alone. I can relate and DD just turned 2. DS(almost 5) was not at all like this so it is new to me. DD has recently started screaming in the car randomly. she will say she wants to listen to certain music and then scream that she wants something else etc. It's hard because we are in the car and there is not much I can do. I have started letting her hold her stuffed animal in the car and she plays with it and if she screams I take the stuffed animal until she is quiet. This usually works well. Last week she screamed once and I said "do you want me to take your stuffed animals?" she apparently had 2 animals and her sippy cup in her hand. She said "mommy take them" and then she proceeded to drop each of them one at a time and politely say "thank you" after dropping each item. Then of course she yelled because she wanted them back. She definitely wears me out sometimes. She changes her mind constantly. She will say she wants cereal for breakfast and after we give it to her she will say "Pancakes" etc. We just stick to what she said first. We are very consistent with her and definitely don't let her run the show...but she sure is trying.
You have the female version of my DS2!!! That is a perfect snapshot of a day in my life including the older DS(almost 5 too) that was NOTHING like that.
When my little guy gets something in his head there is NO distracting him. That entire distract a toddler concept? Yah right. I've worked daycare privately and in the school system and I have never dealt with a kid like him, but obviously there are more out there. That makes me feel a little better...