I think the most important thing to teach kids in terms of history (and anything, really) is to analyze sources. Primary sources, definitely, but also secondary sources. Every source has biases. What are they? Why do they exist? What is in the author's history, background, and purpose that is leading the author to write this way about this subject? What is the author getting out of this? How could you look at the subject being discussed from a different viewpoint? If author A says one thing, and author B says another thing, why?
Professors who have dedicated their entire lives to a subject write long books about this, and children definitely don't need to be taught to pick everything apart at that level. But a healthy skepticism about anything they read, and an understanding that everyone has biases (personal or cultural) goes a long way in creating a historically educated child.
In most cases, history is written by the victors and it's simple enough to dissect bias and where it appears and why it's convenient. In a few cases, it's written by the losers (see, for example, Gone with the Wind's pretty pronounced effect on our cultural understanding of the Civil War and Reconstruction). Historical jingoism sometimes causes backlash which is just as inaccurate (for example, the "Noble Peaceful One-With-The-Earth Savage" American Indian trope that often gets trotted out particularly for kids history books, which is so unbelievable patronizing and infantilizing). Even the "right" side has its exaggerations and myths: the Rosa Parks story that usually gets told is that she was just a tired old woman, when, in fact, she was an established activist well aware of what she was doing and very much meaning to spark exactly what she did spark. The innocent old woman who accidentally sparked a revolution makes a better story. She gave interviews until the end of her life basically saying that it really bothered her that she was going down in history as just an unassuming and unaware victim.
The Revolutionary War subject mentioned above is a really fascinating topic full of misinformation. As Abimommy said, the taxes we've heard about being so unfair were to pay off the debts of the French and Indian War, which had been entirely about protecting the colonies and which the residents of England had been paying for decades with no relief in sight. Up until this point, the colonists had paid no taxes whatsoever: all of the infrastructure and administration and salaries and protection were being paid by taxpayers who lived in England. Popular opinion in England was divided, and the majority did NOT support any effort to retain the North American colonies: they were a huge financial and bureaucratic pit with little return other than wood and furs. which were getting really hard to find at that point. The colonies in southeast Asia and Africa were already proving far more profitable and worth the effort. Most of the soldiers who fought on the British side were mercenaries, because England didn't even really think it worth it to devote too much of their naval and human resources. Cornwallis's next gig was as the Governor of India: not exactly the job you'd give to some truly shamed military failure who had lost a great asset to the Empire. George III was practically the only one in government really gunning to keep the colonies, and he was already insane at that point. His obsession with keeping the North American colonies was widely seen as a perfect example of his insanity. Good luck learning much of any of this in a history class before college.
But all countries need a creation myth, a shared heritage with which to rally the troops. Sometimes those goals are laudable, sometimes not. Sometimes they're harmless, sometimes they're not. Brits basically just roll their eyes when they hear about how devastated England was to lose our bickering little backwater: our Revolution is seriously just a blip on their long history. Thanksgiving was resurrected during the Civil War to give a shared heritage to North and South. The turn of the 20th century saw a huge prominence placed on colonial heritage: this was largely to differentiate "real" Americans from such interlopers as the Italian, Jewish, and Russian immigrants who were coming in large numbers. And going to "take over the country" and why couldn't they learn English like REAL Americas and they were having too many children and taking up too many social services and soon we'd all be speaking Yiddish and be forced to convert to Catholicism and soon there would be more Italians and Jews than white people! Sound familiar? Some things, unfortunately, never change.
Wow I went on for far too long in this comment
Sorry about that. I think that there's not much you can do about what's taught at school. Teachers' hands, in many cases, are tied. History gets short shrift in most classrooms anyway. Until middle school, history is often just random little units taught around holidays or specialized months, with no coherence.
At home, I would teach your kids to read critically. I would make sure that they have access to a range of resources. I would check out the magazines Cobblestone and Calliope and see if they have any back issues that spark your interest: I find those magazines really well done. I would talk talk talk, as another poster recommended. This means that you have to make sure you've read a lot on the subject beforehand, so that you can be prepared to really have a discussion when something comes up. "Why do you think it says that? You know, I've read that actually X, Y, and Z is what happened. Why do you think your book says this, and my book said that? How do you think we can find out more?"
I think that the best way to make kids really think about history and culture is to travel. My parents were always taking us to random historical sites and little museums, and I think that it really fostered in me an appreciation of the human aspects of history.