Social security payments to children.

 If the Social Security (SS) payments, including SS disability, were under his/her SS number (as they usually are), it does not get reported on your return. If it does need to be reported, it would go on his/her individual return. If that was his/her only income, it does not get reported at all. He does not need to file a tax return. 

SS is only taxable & reportable when added to sufficient other income. Social security only  becomes taxable, when his income, including 1/2 his social security, reaches $25,000

If my wife and I file a joint tax return and he is a dependent on our return, would his SSD payment be lumped in with my wife's earned income and it bumps it up passed that threshold, does it then become taxable?

No.  You do not report his income on your return.  If that is the only income he has then he does not have to file and nobody reports it.