One thing I try to make sure I do if we are going someplace where something regular takes place, i.e. getting circles at the HFS, and it is NOT going to happen this time, is make sure I say something prior to ever leaving the house. For example, We are going to the movies. The theater is next to the HFS. I know you like going in there but because we will already be pressed for time after the movie, we can't go in this time. But, I am planning on going on X day.
I usually do not get asked. My oldest, 8.5 years, does sometimes ask just to see if perhaps I am up to negotiation. But, they often just let it slide knowing the next time we are going. We have been to the movies once before. I was on very limited funds. I let them know before setting out that we would NOT be buying anything at the movies. We would have drinks and snacks in the car for afterwards. They picked out those items from choices we had at home. It saved a lot of hassles in the theater.
I understand there are times when they want things, when they are overwhelmed, etc. But there are also times when I have to stand my ground. But, I have found that if they are prepared with all the information they need to make a decision prior to be right in the middle of something, we all do better.
I have found myself in the middle of such tantrums for whatever reason (preparation does not always work, especially for my oldest), I make sure we are someplace where no one can be hurt. Often, that means a locked car. I sit quietly in front and let the upset child cool off some in the back. I repeat often if they need me, they can come get in my lap. Once they have burnt up some energy, they usually do come snuggle. Then, when they are ready, I put them in their carseat. If I am alone with both girls, it gets more complicated. It is hard not to exclude the calm child but in turn no pay her too much attention and add fuel to the fire. I have found that if I try to "force" myself physically or verbally on the upset girl, it makes matters worse. I may physically remove the child to a safe location but then, I try to give them space making it clear I am here if they need me. My oldest usually wants me sooner, though it has been a long time since she has had a full-on tantrum. My youngest will scream it out alone longer but then want to snuggle longer afterward too. I also try to make sure that they do not feel wrong by what they are doing but I do try to talk with them later to let them know they are more appropriate ways to make their "argument" about what they want. And, now, with my oldest, we discuss what she might do differently to be more effective. She is learning. She can tell when I am open for negotiation more and more.