I used to live in Yuma AZ and they were hard-nosed about birth certificates. I think you may have to reschedule until you get their birth certificates. Social Security Cards get stolen all the time and apparently they want them but not by themselves. Shot records, you should call and check because some places will take shot records if it's from birth. I'd call them and ask and if they won't then you can reschedule :)
I agree with Korie B. Go to the county's website they were born in or call and order a birth certificate. It's going to be about $25 each. How do I know? because I've ordered mine before hehehe. It sucks but you will need them at some point so get a safe place for them. lock box, a specific shoe box or something like that.