Sounds like an off morning. She sounded tired and cranky and you were rushed...never a good combination.
My son is only 2.5, but yesterday (after staying up for 2 hours to yell the night before), my husband had to pry him out of bed, he had a meltdown for no reason. Wouldn't get on the potty, then wouldn't get off, the water in the sink hurt his ears, etc., etc. Then he didn't nap!
This morning, he woke up happy and was very cooperative. When he was getting dressed, he asked for help. My husband was impatient because my son woke up early and he hadn't gotten dressed yet, and went into the, "just get it done" mood. I was nursing, but sent off my husband and had my son sit on the bed. He asked for help and I told him that I knew he could do it, and then cheered when he did.
I think that if you are both having off mornings, it sucks. It is much easier if you take turns. :)
Oh, and in the car, you should talk about what happened that morning. Why was she so upset to get out of bed, does she need to go to bed earlier? If she can't wake up in a good mood, she might need to? You can talk about a mom's responsibility, and a daughters, and plan for how to make it better tomorrow. You can talk about this on the way home too.