I got our visas in 2002, so it might be different now. But I was told that my kids did not need to come in person to the Consulate, but that they did need to be present in the US at the time of application (obviously they would be because I needed to take their passports to the Consulate!).
As for your older son, he'd have to be moving with you as your dependent to secure the visa. And if he turns 18 in April (i.e. before he finishes US high school), he can always apply for a student visa to come study in the UK. That would be completely separate from your visa, though.