I don't have kids, but I don't know H's SSN by heart, nor does he remember mine. I didn't know his mother's maiden name when I got asked that once as a security question, so, yeah.......
I know my H's and he knows mine. I need the last 4 digits of his for a lot of our accounts, and fortunately for me, the last four digits are exactly the same, only the last two numbers are swapped.
H is good with numbers, so he'll probably have LO's SSN memorized long before I do.
H knows all of them. I call him in a panic any time there is a form to fill out that asks for it. I cannot remember them for the life of me and H's is super easy.