Tantrums in public are awful and I don't think there is any perfect way of dealing with them. I usually try distraction (ignoring is not always possible in public because I don't think it is safe to walk away from my child - if they are in the pram, strapped in and safe then I do ignore for a little bit and just keep shopping) because there are lots of things to look at and distraction can be easier in public (sometimes). If distracting fails and they persist, I remind them that they need to stay calm and use their words if they want something. Sometimes this works. If tantrums persist, I pick them up and take them out.

I usually take my double pram into shops with me although DD does walk. If she cracks up or refuses to co-operate, I put her in the pram and tell her when she is calm we can talk about it and she can come out. If she goes into the pram a second time, she stays in there for the rest of the shopping trip. She can still be screaming for a bit, but I have been doing this with prams and trolleys since she was small and find that it didn't take long for the length of her tantruming to decrease if I just ignored her. Within a few weeks of starting it, her tantrums and screaming were lasting less than 30 secs.

DS is a different kid and has tantrums about different things when we are out. Usually because I take him away from something while he is looking at it. I do what you did and warn him that we have to keep moving so finish having a look. I then get him to say goodbye to whatever we are looking at. Sometimes he flatly refuses and I say goodbye for him "Bye trains ... see you next time" and keep my tone light but definite.

There is a lot that you can teach your kids by your tone - if you tone goes upwards at the end of a sentence 'Time to go' - it sounds like a question. If your tone goes down it sounds like a statement. Try it outloud. If you are accidentally sending messages in your tone like you are asking a question, your toddler interprets it as a choice. If you say it more like a statement it sound more definitive and I find they are more likely to follow even if they don't want to.

Other strategies are with your instructions saying 'thanks' or 'thank-you' at the end rather than 'please'. Please can also sound like a question though there is something about being thanked in anticipation where we sub-consciously feel that we should do what has been said.

If you are leaving something like the trains and she doesn't want to go, you could also try asking a question about what you are doing next as a distraction. Questions get them thinking. I usually say 'Do you know where we are going now?' or 'Mummy needs to find ... can you help me? Can you see ... anywhere? Hmm ...' I find this kind of dialouge really useful in distracting them. Having a conversation with myself until they are engaged can be really useful.

I know totally what you mean about people looking at you when your kids throw tantrums. It is not nice, but I try not to let them get to me. I find it very amusing that if my DH takes our kids out and they throw tantrums, he get lots and lots of sympathy and understanding from people, where I get comments and rude remarks because I am not controlling my kids. Apparently when men take kids out by themselves, they are really overexerting themselves and people are very obliging, when women do it, we are just fulfilling our obligations. It is a big generalisation to say that, and it is not true of everyone, but I think that a large part of our society think like that on some level (even if it is subconciously).

I hope your DD's tantrums settle down soon - it would make going out a lot less stressful.