How do I go about locking my child’s social , keeping unwanted people from trying to claim her

[DoninGA]

You can get an Identity Protection PIN from the IRS for the child.

Go to this IRS website for an IP PIN - https://www.irs.gov/identity-theft-fraud-scams/get-an-identity-protection-pin

[Opus 17]

For taxes, you can opt-in to the IP program.  Just remember that the child will need to use the IP pin for life, and the IP pin changes every year (the IRS will mail a new one in December before the start of a new tax season.)

If this is about more than just a relative trying to improperly claim your child, and you are having other problems you can contact the 3 main credit bureaus to put a lock or freeze on your child's credit report, making it more difficult for people to open accounts in their name.  Freezing a child's credit report is a little more difficult than freezing your own, you probably have to call instead doing it online.  But it can be done. 

[Hal_Al]

Q. What do I do if somebody does claim my child?

A. If someone else claimed your child inappropriately, and if they file first, your return will be rejected if e-filed. You would then need to file a return on paper, claiming the child as  appropriate. The IRS will process your return and send you your refund, in the normal time. Shortly (up to a year) thereafter, you'll receive a letter from the IRS, stating that your child was claimed on another return. It will tell you that if you made a mistake to file an amended return and if you didn't make a mistake to do nothing. The other party will get the same letter you did. If one of you doesn't file an amended return, unclaiming the child, the next letter, from the IRS, will require you to provide proof. Be sure to reply in a timely manner.

Winner gets the tax benefits; loser gets to pay the IRS back with penalties and interest.  The custodial parent almost always wins. The IRS goes by physical custody, not legal custody. The non-custodial parent can only claim the child as a dependent if the custodial parent gives permission (on form 8332) or if it's spelled out in a pre 2009 divorce decree.