‘Problem child’ vs. being a 3 year old

Our daughter is extremely lively which I love. However, she can hop over the ‘troublesome’ line very quickly. First, her patience is non existent. If I say can you wait one second please? she will completely disregard this and get upset. Should they be able to acknowledge time by now? Another example, I had to move my car from the driveway to the front curb- literally 20 feet away. I ask her nicely to sit on the porch and wait, I described what I needed to do for. She gets mad and insists I take her. So I had to put her in the car seat to go on a 10 second car ride.

Also, being carried around. If I don’t carry her to the fridge to get her milk she will throw a tantrum. I ask please hold my hand we will walk there together- she’ll go cray. My back is literally about to break she weighs 35lbs. I can’t imagine having an actual baby right now she wouldn’t be able to cope I don’t think. Anyway I’m just concerned she’s behaving as a normal 3 year old would or not.