Exactly this. I'm a US citizen who worked for a few years in Canada. Don't listen to OP - the tax issues are monumentally major.
Most countries tax based on residency. You earned money in your country of citizenship, you pay taxes there. You earned money in another country, you work out the taxes over there. Your native country doesn't get involved. This is why Canadians working in the U.S. for part of the year have to be able to document the number of days they stayed there. If they're in the U.S. for more than 183 days, they're considered a U.S. resident and don't owe Canadian taxes.
The U.S. taxes based on residency and citizenship. You earn money anywhere in the world, the IRS expects you to pay U.S. taxes on it if you're a citizen. If your kids become U.S. citizens, ignore the U.S. tax filing obligations for 20 years because they're living in Sweden or wherever, then when they're in their 30s and married and have kids they decide to visit the U.S., the moment they try to step foot into the U.S. the IRS will nail them for back taxes on everything they earned for the last 20 years. (Ok, there's probably a statute of limitations, but you get the idea.)
A lot of Americans living abroad work their butt off trying to renounce their U.S. citizenship just so they don't have to deal with this tax hassle. Do not subject your kids to it unless they intend to live in the U.S. (Some U.S. states do the same thing. California is notorious for it. If you were living in California prior to taking a job in the U.K., California still considers you a "resident" since you didn't move to another U.S. state, and expects you to pay California taxes on everything you earned in the U.K. Even California kids who go to college out of state and don't formally establish their residency in that state have gotten nailed for it when they work a part-time job while at school.)
The U.S. has tax treaties with most developed nations, where taxes paid in those countries on earned income (i.e. wages) can be applied as credit to taxes the IRS says you owe. Since most countries have a higher tax rate than the U.S. Federal taxes (U.S. Federal + State ends up being about the same), this usually means you won't owe the IRS any taxes on earned income. But they still expect you to file a tax return every year. And if you've got unearned income (e.g. interest on a savings account, stocks), you're probably gonna end up double-taxed on that (in both your country of residence, and by the U.S.).
Unless your kids are going to live in the U.S., don't do it.