She should speak with an immigration lawyer, explaining all facets of her education, experience, and family relationships, to get the best answer - because there are several possibilities for her. The question of the child's father presents a few problems, and should be discussed as well.
One possibility is an H-1B visa for a professional job such as teaching (requires that she have a Bachelor's degree or the equivalent, and that the job requires a Bachelor's degree). These visas are typically numerically limited with an annual cap of 65,000 available, and she would need to apply in early April to try to get one of the available ones through a lottery to begin on October 1, 2009. Some school districts are exempt from the numerical limit, though in some cases this is being challenged by USCIS right now - so it's difficult to say if an H-1B would be available earlier. Her son could come on an H-4 derivative (immediate family member) visa, but not the child's father if they aren't married.
Next question: what is your immigration status? If you are a U.S. citizen, when did you acquire citizenship? She may be eligible for permanent residence based on your sponsorship - but this would need to be explored further. Depending on the circumstances, she may be eligible but the process may take too long to be practical for her near term plans, and again without a legal marriage the child's father wouldn't benefit..
The child's father presents the biggest problem - as I mentioned, if not married to your daughter he would not be eligible for any derivative status, and without a degree or very significant experience in something there would be few visa options. There may be possibilities, but a qualified immigration lawyer would need to review a detailed resume for him.
Again, your daughter and her boyfriend should speak with an immigration lawyer to get a detailed evaluation.
Another option, although providing only a short term stay is a J-1 Exchange Visitor visa. Although there are many facts that will affect her eligibility for this visa and need to be discussed, she could hypothetically qualify for an 18 month training program under the occupational category of education. Note however that certain occupations fall under a Skills List which may in turn subject your daughter to a 2 year home residency requirement which would make her return to the U.K. for two years prior to being eligbile for another visa to enter the U.S. Note however that there are certain waivers availalbe to remove the 2 year home resiency requriement.
It would be a good idea to speak with an immigration attorney to get some advice as to your daughters specific situation.
Also, Mr. Pretorius omitted a different type of J-1 Exchange visitor program especially for teachers who agree to teach in a US public elementary or secondary school. These do not have the limitations on "training", they are explicitly full-time positions for experienced teachers, sponsored by certain organizations accredited by both the US State Department and the Board of Education in the state where they place teachers, and they are valid for 3 years. Her son could accompany her in J-2 status if she were to come as a J-1 Teacher.