I have tried to find you a link to a good explanation of the "Disability Family Maximum" computation, but have not been successful, so I will give you a vague answer and I cannot vouch for it being 100% accurate.
When a worker has the bare minimum of credits to be insured for disability, in cases where the worker is younger, the computation of the family maximum will not yield the same result as a person who has worked a substantial number of years and has many credits beyond the bare minimum needed to be insured. Often, in the bare minimum quarter cases, the monthly benefit paid to the worker (you) equals the amount payable to the family (your children) so there is nothing left to pay the children.
My guess is that you did work enough to be insured for SSDI, but did not have substantial earnings or years of work.
If you can get a Title 2 Claims Rep on the phone (like the one who took your original claim) you might get a more detailed answer to this question. It may also overwhelm you because it is a complex computation. If you have not filed an official application for children's benefits, you could do so now and you would then get an interview with a Title 2 Claims Rep and an official denial notice. I would suggest an in person interview in your local office, face to face. You can see the numbers and probably get a more satisfactory answer. You still may not like it.
Also, there was never any order by President Bush to not accept qualified applicants like another poster suggested. Wrong, wrong, wrong.