I'm starting to panic..

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.

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!!

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.

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.)

Sorry...daughter and SiL.

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.

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

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.

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?

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.

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

This is what Google says about gun law in the States

All 50 states allow, at some level, concealed carry, but some states are considerably more restrictive than others. California, Florida, Illinois, Texas, South Carolina and New York (as well as Washington, D.C.) are the only states to prohibit open carry of handguns in public.20 Nov 2014

Your SIL is American, and it is quite natural that he might want to move home and give his child the kind of upbringing he had and his wife the kind of home he grew up in.

Presumably, he has family he misses? Perhaps this, and not secondary schooling, is the real issue.

In your place, I think I would have a quiet word with SIL concerning health care in the US and a quiet word with DD pointing out that the school system is definitely not better in the USA than anywhere in Europe or the UK.

After that you just have to let them make up their own minds, and it does depend a great deal where they intend to go, how worried you need to be.

Good advice here and follow grannyactivist.
The media tend to make us think everything is bad in the US but that is just so far from the truth. There are many Brits who have emigrated to the US and loved it.

Say nothing. Your son in law is American. It is not as if they are going to a country where neither are familar with the health care and education systems. His experience comparing what the two countries have to offer must have had a bearing on their decision. I doubt local senior schools are the prime reason as there would be closer solutions. If your daughter seems happy with what she and her husband are considering then you have to let them go ahead without interference. If she needs to know and plan she'll be doing her homework. Sometimes a change of location and a new start is just what we need to get past difficult times.

MiniMama.Many of us have to watch our children fly to a different life overseas and I endorse what Matelda says. Each state in the USA varies but I have nothing but praise for the education and medical treatment my family have received since they moved to that country taking my grandchildren with them. Children, now adults, making their own way in a country that, contrary to the doom mongers, have many opportunities there for the taking. No they don't have a NHS. People take out insurance but I can assure you there are those in the U.S who do receive benefits depending on their circumstances. The U.S reward those who help themselves and you cannot condemn something unless you have had experience of it. As for the crime rate comparison has to be made when you measure the size of the US to the UK. Yes they do have easy access to guns however the UK is not as safe as we would like it to be. I can understand your concerns I have been there but don't let your daughter see these concerns. Give her your blessing and what would stop you from experiencing what that country has to offer your daughter once she has settled.

I would be a bit worried that she thinks she can escape her problems by going to the USA. And unfortunately they will follow her. On the other hand she might flourish in a new environment.
At the end of the day it's their decision.

MiniMama I think you've fallen into the trap of extrapolating the news to the whole country! Yes, people have guns and yes, there have been tragic shootings but the US is a vast country and 'mostly harmless' (to quote the Hitchhikers Guide). As OP points out, if it's with your SiL's job then he will probably have health insurance and I'm sure the mental health care is as good as, if not better than, here if they can pay. Does she want to go? Is it him pushing for this? Could they come back if she can't cope?

Agree Mandyone

In addition, I was not aware that the education system in the the USA was ‘better’ than what is offered in the UK, in fact, if anything, I thought it wasn’t so good.

I think grannyactivist has covered the main points for consideration, and a few others have added to that.
What I would be most concerned about at this stage, is would your daughter, who has endured so much already with Post Natal Depression, be able to cope both mentally, and physically, without the nearby support of her parents? Especially as she has only just come off the antidepressants. That would be my major concern, as I have a daughter who has suffered PND and I know firsthand how much support is required in this situation.

Marking exams from abroad, including the States, has taught me how superficial and limited their education system is. I wouldn't let my children be reduced to the education system in the USA.

So many many things to consider first. Has she stayed for any length of time in the area they may want to live? Does she really like it? There would have to be more than one reason to up sticks and go so far. There are ropey and underperforming schools everywhere. Similarly there are great schools everywhere.
Plenty of things to talk about here!
As others say, if you try to remain neutral, you can help her explore the possibilities and pitfalls.

Several members of my close and extended family have moved abroad, including to the United States, and sometimes permanently. I think that, without exception, it has been the making of them. Facing up to new challenges has made them stronger, more resilient people. You must let your daughter make her own choice, but, if she goes, be sure to set up appointments for regular meetings on Skype or similar. And, if you can, start saving for the fare.

A very important issue for them to consider is health care for all the family. What sort of cover does her husband have, is it linked to his job and if so is it a stable job? If you have good health care the system over there is far superior to the NHS, ie shorter waiting times and hospitals over there are far superior to ours. I was hospitalised for 11 days when in Florida a few years ago, I had an en suite room, the nursing care was wonderful as were the doctors and physiotherapists. The picture is very different if you do not have a good healthcare package.

Another issue of course is schooling for the children. Some schools in the USA are very scary places, they need to do the research.

As sodapop said you can have a great life over there but it all rests on whether you are financially stable.