It's shifted in a generation I think. Because we have a better understanding of what little children (up to about 3) are capable of, we give them more leeway and as a result tantrums below that age are pretty easily contained, avoided or distracted.
A generation ago you'd be encouraged to "nip it in the bud" using punishment/threats/ignoring at around age 2, which means much more fighting at that age with a child who is not developmentally able to control themselves (hence, terrible twos). These days it gets delayed a bit so you have the normal tantrums at age 1-2-3 and think no problem, I can handle these, easy. Then they get to 3, 3.5 and it all explodes everywhere because they are less distractible and (sometimes) because you haven't actually been setting boundaries but just distracting.
It sounds like what happened was:
She was tired, and hungry (you were about to go to lunch) so she has a low bar. It can help to avoid high-stress or high-excitement situations when she is tired and hungry, also you can keep hunger at bay with frequent snacks - this is a good idea on tired days. (Other things that can cause her to be near the "volcano limit" are being low on attention/connection from you, being bored, being overstimulated by TV or something very exciting or a noisy/crowded/bright environment, coming down with something, big changes happening in her life e.g. house move/new baby/new school etc.)
The transition (ending one activity, especially a fun one, and starting something new) was very hard for her as they often are for young children. However, younger children are very go with the flow and in terms of transitions they are momentarily upset but then quickly forget about it. (Think about how a baby cries when you strap them into a car seat, but are fine as soon as you get moving.) Three year olds get fixated on one thing and cannot move on from it until they have processed it. Whatever your distraction is will seldom be shiny enough (and if you get into the habit of ever-more-shiny distractions this can become a problem in itself). It can help to prepare her for the transition in advance, so explain before you even arrive at the place the sequence of events "We will go to the garden centre, you can ride on the car, then we will go to the till, then we will get lunch and come home." Remind her when she is getting on the car that the activity will end and what is coming next. Then give her a warning just before the end. I always find it helps to give a number as well so something like three more laps, or a choice e.g. if in a park, we have time for three more slides or five pushes on the swing, what would you like to do? When it is over, don't rush her away, give her (a little) time to get out by herself, but don't linger too long either. Maybe encourage her to say bye to the car, or something else she associates with endings, and remind her that you can come back another time.
When she was upset about leaving, you acknowledged her feelings (the car was fun) which is good but then tried to jolly her along to the next thing. This works really well with 2 year olds but stops working quite as well at this age because they get so fixated and because the feelings are overwhelming. There is not really a huge amount you can do if it explodes in a big way - you can spend a little longer with giving space to her feelings, giving wishes in fantasy (from HTT) but when she's tired and hungry on top then the best thing to do is just remove her from the situation to a safe place to calm down.
You don't need to be stricter in terms of punishing the outbursts etc. That likely won't help, but it might help if you are currently relying on distraction to avoid big feelings when you set a boundary, to read some of Janet Lansbury's stuff about boundaries. You mention her often shouting no or reacting to being told she can't do something etc, and I wonder if you've previously just been quickly moving on to the next thing when this happens and that is the part which isn't working any more. She has noticed that there are boundaries, and she is not happy about it! That's absolutely fine and good - it just takes a bit of a shift to get ypur head around supporting her through that.