How do you make sure no one is using your kids SSN before you file so you don't have to get shorted thousands and have to amend the return.

You cannot prevent someone from using your child's SSN if they managed to get hold of it.   But if someone else claims the child who is YOUR qualifying dependent, then if your e-file is rejected, you need to print sign and mail your return.   You do not amend it.

Someone else claimed my dependent and my return was rejected

If someone else claimed your dependent already, then your e-filed return will be rejected.  Print, sign and mail your own return which claims your dependent.  Mailed returns are processed differently by the IRS.  It will take some time (maybe even up to a year) but eventually the IRS will contact both parties and sort out who could rightfully claim the dependent.  The person who wrongfully claimed the dependent will face repayment of refund $, plus penalties.

When you mail a tax return, you need to attach any documents showing tax withheld, such as your W-2’s or any 1099’s.  Use a mailing service that will track it, such as UPS or certified mail so you will know the IRS/state received the return.