Her withholding the social security number and cards in itself is not a violation of the custody order unless the order actually states to share documents such as the social security card. If she continues not to, you could possibly seek a petition for contempt of the custody order with the Judge who signed your custody agreement, stating that the legal custody being shared is not being complied with since you can't make medical or legal decisions on behalf of your daughter becuase the other parent refuses to share necessary information.
It would be best to hire an attorney and seek their advice on the issue. Best of luck!
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