Toddler Behavior When Others Are Around.

Separate them. They feed off of each other misbehaving. Strength in numbers. If you are going somewhere that they need to behave, take only the one that needs to be there and leave the other one with a grandparent, a neighbor...Once you establish you are in control of them independently they will likely start respecting you when they are together. Plus you will learn in these little windows of time how to pull the reigns in on the individually. They may feel like one unit of destruction, but they are two different kids acting in unison.

They sound more like typical kids to me! Kids who want attention focused on them and can only wait for so long and get fidgety and as soon as your attention is focused elsewhere (i.e. talking to someone else) they start trying to get it back on themselves.

This is when you start teaching them not to interrupt - I've been working on my 3 year old with this. As soon as I start talking to someone and she butts in, I very firmly tell her, "Excuse me! Mommy is talking to Daddy right now, and you will need to wait your turn. Thank you. " She's been going to preschool and understands the concept of taking turns. If I'm on the phone and she starts cutting in, I give her the "one minute" finger and just tell her "Wait!" She's getting better, but I also try to keep conversations short, before her patience runs out.

As for discipline in general, maybe it would help to read up on some discipline techniques that you can apply more consistently and should be more effective. Such as "How to Behave So Your Preschooler Will Too" by Sal Severe. However their dad should be backing you up on discipline as well - if you asked him to take the kids out of the exam room when the doctor was there, he should have done it. Or had found some other way to keep the kids occupied while you were seeing the doctor.

"acting up", when you have company, use the phone or are otherwise distracted continues well on into teenage years! I remember my middle DD, if she wanted me to give a favourable response to something I'd likely say no to, she would wait for these opportunities.. I eventually set a rule that no matter what she asked, if I was busy and distracted, the answer would be NO, and if she weaseled a yes at these times, there would be consequences. They can be uninterested all day, but the minute your focus is on someone else, they want you, or start up some charming antics.

You have to be firmer and more consistent. That's always the answer, the same way, "You have to cut calories and exercise more" is always the answer to weight loss. The kids aren't always perfect when you're alone if you really analyze it. There are plenty of times when you ask them to stop doing something, they don't, and then you don't enforce. If you're like any normal mom, in the comfort of home, you let things slide. If you ALWAYS did address everything, they would not do it in front of others. If they tried it, and you enforced it there too, they would see its not OK.

My kids would be doing all of these things too if I had not been very diligent and firm from a very early age. I always enforced "no interrupting" immediately when they started that. I always enforced "no acting up when I'm on the phone" when they started that. Yes I had to interrupt the call, enforce discipline, and call the person back, but if I hadn't done that, they never would have learned to respond to me giving them the "signal" like they do now. Yes I had to say, "excuse me" to the person I was talking to, remove them, and enforce discipline for interrupting if I had warned them and they continued. But if I hadn't they would have kept doing it.

When the kids climbed to the front of the car and railroaded your conversation, they should have had a clear explanation of what they did which was not allowed, and a firm consequence afterwords so that the next time you warned them, they would understand they had the choice to be polite, or the choice to get a consequence.

Very few kids need almost no discipline. Most kids need lots. Some kids need tons. Be firmer and more diligent and you will see it pay off. Also be consistent with the SAME thing (firmest) after ONE WARNING, or they will gamble much longer and wait for ten warnings every time until they see you getting mad. Don't get mad, just act firmly and immediately after one waring. Once they get it, they'll avoid the discipline and form correct habits.
Also, don't try to discipline specifically for all different things. With numerous kids and numerous things, it's too much for them to remember in any given day. Just teach that they have ONE WARNING to do whatever you SAY. That goes for interrupting, tearing up the doctor's office, climbing on you when you need your hands free WHATEVER. Thousands of things per day. Same firm consequence, one calm warning, for whatever you say, every time. It will be a lot of work at first, but it's the fastest way. They will improve and it will be worth it. You'll soon know the relief of saying, "Stop" and seeing them stop. Start at home. Make sure dad steps up too and it will go twice as fast.