Hi, and welcome to the forum.

Where to move in America is entirely related to where you can find a job. The way the visa process works for the US is that in most cases you have to be "sponsored" by either an employer or a direct family member (parents, children, adult brother or sister). And "sponsoring" (called "petitioning" in the US regs) costs the person or company doing it.

Unskilled laborers they don't really need more of over there, and chances are you will find it difficult to get jobs with no university and no experience in a needed trade. To have any chance of a working visa for a job with promotion options and a good career path you really need a university degree plus at least a few years' experience in the profession. The other "gotcha" is that, under some working visas, the worker can bring family with (spouse and children), but the spouse will not be eligible for a work visa.

As far as nurseries and schools are concerned - the public schools are locally controlled and most public school districts these days start with kindergarten (age 5 or so), though there are still districts that do not include kindergarten. Nurseries (or nursery schools) are privately owned and operated, and so you normally have to pay to enroll your child.

As someone else said here on the forum recently, where there's a will there's a way. But it will take some time to get the sort of training and experience you need to qualify for a visa, and it pays to have a clear picture of what you're up against. Do check the website of the US Embassy in London Visa Services U.S. Embassy London - they have quite a bit of information about the various types of visas and the process for applying.
Cheers,
Bev