It doesn't matter how much Social Security income your children receive, or how much of it is taxable. What matters is whether you actually use the money for their support. If you put some or all of the money in the bank or into investments, that is not money that's used for support. The IRS can't see how much of the money is actually used for support.
As you can see from the support worksheet, support includes housing, food, clothing, education, child care, medical care, and other things. It seems to me that $12,000 a year would be nowhere near half of the cost of supporting a child, and you said that not all of it is used for support. I think you should go ahead and file as head of household with two dependents. I don't think you have to worry about raising any red flags.
This is just my opinion, of course, and I don't have all the facts. If you're worried, you might want to consult a local tax professional for advice.
