To solve the problem of him getting into the car, we and a few others recommend using choices phrased like:
"Do you want to get yourself into the car or do you want me to put you in the car?"
Either way, he gets in the car, and usually a bit calmer as he's "made a choice".
Longer term, reward charts will help. Getting a sticker every day on the chart that he gets into the car well is a good way of reinforcing good behaviour.
But ultimately, he's two. Two year olds will push boundaries. They just need to understand that sometimes that's going to hurt them or deprive them of something they would like. "Get in the car or you'll have less time with your friend/grandmother/giraffe" or wherever you're going. "Get in the car otherwise I won't have time to buy pudding for tonight's tea".
They do pick up on parent's frustration well as well. If they work out that if they do X you react with Y they'll do it. So even if he's really hanging back and mucking around, pick him up and put him in the car as if nothing's happened and talk about something else. Don't make it a big deal with your emotions as well as (as you're doing) not making it a big deal with your physical actions.