I agree with Curlew - you need to stay in control of YOUR emotions. Simply accept that you cannot control whether you child kicks off or not, but what you CAN control is what you do; the tantrums will end quicker if they get the child literally nowhere, hard though it is. Forget the naughty step if you have a child with the nouse to get up! You'll have to use another room. And don't worry about whether there are interesting things in there, this isn't about 'punishing', it's about seperating yourselves so that there is nothing to 'feed' the tantrum; if she finds something to amuse herself, great! she'll calm down all the quicker.
If you are out and about, use the threat of time out in her room when you get back, this worked with my ds anyway.
And when it's over, as Curlew so wisely said, your job as the adult is to (pretend to) forget all about it. You don't need an apology in my view - children shouldn't have to apologise for being children and still being at the stage where they have strong emotions that they need to control. Just move on; it just makes kids feel stressed I think if the previous outburst is dwelt on.
With the car, I am out of my depth as never had this with ds. But I think the same rules apply, you'll have to threaten time out when you get home, then ignore like mad.
But then again, desperate's trick of threatening to make child walk home seemed to work!
best of luck, and yes it really will get better!. I always try to keep a nugget of sympathy for my ds when he really tantrums - he can't help it and it must feel horrible.