I have 2 SSA-1099 forms, one for me and one for my child. Do I need to enter both of them? How do I enter a second form?

You do Not enter the child's SSA-1099 on your tax return.  If the child has no other income they do not report the benefits received on a tax return.

Do not enter the SSA1099 for your child on your own tax return.   Someday if the child has other income  (after school job, etc.) and is filing a tax return, for that tax year he will need to include the SSA1099 on his own return.  Until then, it does not get entered anywhere.

No.

You don't enter your child's SSA-1099 on your tax return.

If your child only has income from the form SSA-1099, he/she is not required to file a tax return.