Medical ID?? Is that for military?
SS# isn't needed. Oh sure, people will give you hell, but if you have to take the boy to the hospital, don't hesitate. I would be helpfull to have. Why is she not giving you that?
You could have your son and her sign a paper, have them do it infront of a Notary, and have it statmped, authorizing you to make decisions while the boy is in your physical custody.(I mean for med, school, and so on)
This mother isn't thinking very clearly. If something happened to this boy, and a medical decision has to be made "RIGHT NOW", you won't be able to. (God forbid bleeding on the brain or something were they have to operate to save his life). That's worst case, but she needs to think. Kids get hurt, sick all the time, and if you can't make a decision when it is needed, the boy suffers.