Born/raised in US (California), lived in Germany for a year in the 70s. I still love living here and at this point wouldn't move anywhere else. BUT I live in a 'blue' state (albeit in a 'red' county) and our economy is thriving.
Healthcare is excellent and our insurance carried over into retirement plus now we're on Medicare, too. This means we have little to no out of pocket expenses. I can see a specialist of my choice at the drop of a hat, no long waits, and complete choice of where I want to be treated. From what I've read on MN, MH care via the NHS in the UK is abysmal. Here, you can get an appointment with a psychiatrist or counselor within days, not months or a year. My son's insurance has a 'cap' of $3000 out of pocket. He was recently in a terrible accident and to date has accrued bills of over $800k (and still in treatment). Of this, he will pay no more than $3000. His insurance will pick up the rest. I'd say he pays around $3500 per year to cover himself and his wife. Pretty good return on investment, I'd say. So, for the most part insurance does do its job here to keep your costs down and your choices unlimited. You just have to be an educated consumer.
Because we're such a huge country the cost of living varies greatly. What may be affordable in the MidWest would be outrageously expensive in California or New York. The same goes for education. Some areas have outstanding schools others you wouldn't send your dog to. You just have to choose where you live wisely and focus on the areas that fit your needs.
As far as violence goes, yes, we have a problem. Especially a gun problem. But by and large the majority of the locations in the US are relatively low crime areas. There are plenty of safe places to live, and others where I wouldn't live for a mint of money. Probably the same the world over. As with all news reporting 'if it bleeds, it leads'. I don't look at the horrific event that happened in the UK today or some of the reports I've read about 'knife crime' and think that every UK city is rife with stabbings or people being mowed down.
My main concern for a female in the US is reproductive rights. I wouldn't live in a Republican state if you paid me if I was a woman for whom a pregnancy is at all possible. If you look at a map of the US with regards to the states that have restricted abortion rights you can see exactly where I mean. And for many women in those states they are 'landlocked', meaning that it's not just a quick drive across state lines to access abortion services. For many of them the journey would be impossible, either financially or due to not being able to 'disappear' for a few days quietly. And many of these states are now poking their noses into women's private lives and passing legislation intending to scare doctors into violating medical confidentiality or providing advice regarding termination options. That, IMO, is the biggest problem facing the US today.
I also think that the issue of child custody for someone who may want to return to their home country in the event of a separation is something to be seriously considered. US courts are unlikely to grant permission for that to happen if the other parent is even remotely 'involved' with the DC. In this case the children also have US passports, making it even less likely that the OP would be able to return to the UK. Shoot, many divorce decrees forbid moving a certain number of miles, to the next county, or out of the state.
All the OP can do is consider the larger picture and hopefully choose wisely.