I'm an E2 visa general holder. Are my kids (6 and 2 years old) eligible to get a social security number too?
No, they are not In order to be eligible for a social security number one must be eligible to work. You can, and should, however, apply for Individual Taxpayer Identification numbers for them with the IRS. This number can be used in lieu of a Social Security number for them.
While this answer is provided by a Florida Bar Certified Expert in Immigration and Nationality Law, it is for general information purposes only and an attorney/client relationship is neither intended nor created. You should seek out qualified counsel to review your case and provide you with advice specific to your situation. Call +1-561-478-5353 to schedule a consultation with Mr. Devore.
I agree with attorney Devore.