Georgia might be a possibility.

You will have to check the details for your country, but typically, the visa is good for a year, and you can extend it by exiting Georgia for as little as a day.

You can get a mailbox service that gives you a street address.

Do you have a bicycle with racks? That could give you more freedom than a car.

Is it possible to go by train?

Education is like an iceberg, in that the vast majority of it is under the surface. My guess is that if you do go back to the USA, your children will have the skills to quickly pick up any content they missed. Functioning in two languages will give then some valuable but hard to quantify thinking skills.

Are high school students where you are behind those in the USA? If not, you probably have nothing to worry about.