I'm starting to panic..

My sister came back from the states and said the schooling over there is not as good as here.

My son lives in Cambridge, Massachusetts, part of Greater Boston and its fabulous. The people are overwhelmingly polite, very hard working, welcoming and friendly. His health care package (usually provided by employers) is outstanding and the hospitals in Boston are world class. There are 52 colleges and universities just in the Greater Boston area alone, some of them top the world league. Its a five and a half hour flight to east coast USA and takes me longer to get to relatives in Scotland. As others have said, the US is a big place and it really depends where your daughter and family are thinking of moving.

I live in the US ....so here's how it really is:

There is way too much coverage and repetitive news about gun violence and it appears to be more pervasive than it actually is. Not denying that it doesn't happen, but the likely hood of becoming another statistic is relatively low.

The issue of schools and healthcare on the other hand, should be of greater concern:

Here in the US, healthcare insurance is very expensive. Most employers will offer a relatively basic (substandard) plan (including senior management) and it's up to the employee to subsidize upgrades to the plan. A substandard plan is one that has very high deductibles, limited providers and low indemnity. Most people pay very high premiums because they don't want to get caught "under insured". Unless you're over 65 or very very poor, the government doesn't giveaway much.

The quality of the schools varies greatly depending on where you live. With very few exceptions, public schools are funded with local property taxes, hence the quality of the schools (teacher salaries, resources etc.) has a lot to do with a particular school district's property values. Sadly, many school districts have become woefully substandard, especially in areas where real estate values have stagnated and there is pressure to hold taxes down.

In the more affluent areas, real estate is expensive and the property taxes are commensurately high. No surprise then that the best schools are primarily found in the most expensive areas to live in. As an example, a home that is worth upwards of one million US$, generates approximately 2.5% of that amount in school taxes (do the math), yearly. A modest private school in N Eastern US costs $30,000 a year; more if it's a boarding school. The most prestigious schools are also the hardest to get into.

So, if D and SIL's move is being driven by the quality of GD's education, they should be prepared to buy a very expensive home in a "premier" school district where property taxes will likely be very high. No matter where they live however, they will also need to spend several hundred dollars a month in health insurance, if employer doesn't offer a good enough plan.

If they're willing to go to all the trouble of moving so they can pay for all of that, then wouldn't it be easier to place her in the best private school near home, instead?

Re. Education in the States... when my children were in the English School of Paris albeit years ago, any pupil coming from the American School had to drop down a year.
I don't think it's changed.

Just leave them to it.It is their life,not yours.

I think that if your son and DiL are adults and use social media and read or listen to the news, that they are are fully aware of what goes on in the world and your fears should not be pressed onto them.
I'm perfectly sure that you don't go on about gun crime, stabbings, robberies etc in Britain when they are out and about, yet here we are not allowed to carry personal guns, unlike US citizens.
Let them make a guilt-free decision instead of having to factor your fear into the equation.

Sorry...daughter and SiL.

My DS and Dil have lived in California for over twenty years. DGC born here. DH & I are here now, on what's become an annual visit. My view is that if you have enough money, plus continued access to good healthcare, you can have a wonderful life here. (But if not, stay in the UK.)

My MiL a teacher, said to me, when you visit a school there is only one question to ask and it won't be answered. The question was: Ask the head teacher how much longer they intend to stay at the school.

I think this rule applies across nations as well as education levels. What is a poor school in England now, could be outstanding by the time the OP's DGD reaches secondary age and a brilliant school in the states now could be failing in a few years.

We live in Manchester and a few years ago we had friends visit from the USA. They turned up quite late one day, apparently they had been trying to avoid driving through Moss Side, as they had heard in the States that it was a "no-go" area because of the gun crime!!

I would agree that you need to separate out your anxieties.
Of course you don't like the idea of them moving a long distance.
I have a feeling that in the UK our media disparage the US in order to make us feel better. I hold no brief for it, but have known, over my lifetime, many Americans and people who have moved there (I live in an area that still has a US base). There are many things about America that I admire and respect, as well as things that are worse than the UK.
There are plenty of excellent schools in the US - I suspect that the schools are one small factor in a lot of other things. One friend did a 'job swap' and thought highly of the year's US schooling that her children had.
I hope your SiL is caring and thoughtful - in which case he will have considered the issue of healthcare insurance, and especially checked the mental health clauses.
I think your grandchildren will benefit from seeing a different culture, and especially connecting with the American side of their family and its history.
I think you need to deal with your anxieties yourself, and maybe some of the US grans who come here can help with that.If you can, put some savings by so you can travel there quickly if needed.
Good luck.