Q. Is the social security income a child receives counted as support provided by the child, himself?
A. Yes, but only if it is actually spent on support. "Support" includes money spent on entertainment. If the child buys himself a video game or a pony, that expenditure is counted as support. But, any money the child puts into savings & investment does not count as support he spent on himself.
As you pointed out, the support value of the home, provided by the parent, is the fair market rental value of the home plus utilities & other expenses divided by the number of occupants. $42,000 / 3 = $14,000 support value, for each child, from the home. Since that alone is more than the maximum $12,000, of support, the child could possibly provide, it's obvious that each child does not provide more than half his own support, not even counting all the other expenses (food, utilities, clothing, transportation, education, etc).
Clearly they are your qualifying child dependents and, as such, also qualify you for Head of Household filing status.
The IRS has a worksheet that can be used to help with the support calculation. See: http://apps.irs.gov/app/vita/content/globalmedia/teacher/worksheet_for_determining_support_4012.pdf
