My grandson and daughter lived with me for over half the year. The courts gave his other grandmother custody and said she can claim him as her tax dependent. Is this legal since he lived in my home for over half the year and I paid for all his care?

The court order must meet IRS requirements. The court order or decree or separation agreement issued after July 2, 2008 can not serve as written declaration to release the claim of custodial parent that noncustodial parent must get release Form 8332 signed by the custodial parent.

Even if the noncustodial parent is able to claim the child, the noncustodial parent gets exemption deduction and child tax credit, but not the head of household status and EITC.
The Custodial parent the custodial parent is head of household and get EIC and any child care credit. Your U.S. Tax Return: Child of separated or divorced parents

If the court is Family Court or Divorce Court, the IRS generally WILL abide by the court ruling if the court ruling specifically addresses who is permitted to claim the dependency exemption.

Make sure the ruling is in fact retroactive, i.e. it covers tax year 2010. If it was just issued, it may only apply for tax year 2011 and beyond, which would allow YOU to claim the dependency exemption on your 2010 tax return.