You don't need the child papers to attend the interview and at this point in time, I don't recommend rescheduling your appointment. Get an official letter from your wife's doctor and midwife, and attend the interview alone. Explain the issue to the consular officer and provide the doctor's letter as evidence during your interview.
We have 4 months to the end of the fiscal year for dv-2011 and you have to realize that it could take between 2-3 months to get a new interview date. It could mean that even if they get a new date for you - all the visas available would have been used up. Another possibility is that you may not get a new interview date before the deadline of Sept 30. Therefore, you have to act wisely not to lose this great opportunity.
If the CO needs further evidence/information he will let you bring it later or give you another date to present those documents.
Am With you bossss