I can completely understand how difficult and scary it feels. I don't know if it helps at all to remind yourself that people travel around the world all the time and are mostly fine. When my kids were born, we were living in my partner's country. The public health system there is terribly under-resourced and in my time there, several people in the community we lived in, including one of my partner's brothers, died from things that they likely wouldn't have in the UK. It was a very poor, very vulnerable community. The private healthcare was better, but nothing like the UK, and it cost a lot on the occasions that we did use it for our kids. (We got a local, private health insurance after the first $$$ hospital experience!)
However, it was truly incredible for my kids to spend those very special years with their family there, and despite living in a poor community with very poor basic services - contaminated tap water, no indoor/flush toilets - the kids were mainly fine. They got the usual bugs and colds that kids in the UK get.
In my job I also organized a lot of learning-exchange trips for high school and uni students from "developed" countries to come and stay a week or two in the community and live in local homes, etc. None of our visitors ever got seriously ill, when people did get ill it was usually a stomach complaint or common cold/flu which they usually had picked up on the plane.
In all likelihood, the worst you or your kids would get would be an annoying and unlucky case of food poisoning. You can pack a mini pharmacy that will be able to cover most illnesses (Imodium, rehydration sachets, paracetamol, Alka seltzer, etc.). In the case that something more serious were to happen, it's highly unlikely that it would be anything so bad that it would prevent you from travelling, so you could just fly home.
If you can find a way to relax a bit about the medical situation, this could be the trip of a lifetime for you and your children. I hope you can get some good travel insurance, maybe research private clinics with A&E depts near where you will be staying (just in case), get all your vaccines up to date, pack well, and go an have a blast with your husband's family!