I do not practice in Georgia but, based on general concepts of child abuse law, you should have a hearing soon on whether the emergency custody of youngest child should continue based on the allegations. Contact a local attorney experienced in dependency and neglect cases immediately and tell that attorney about your mother's lies and the reasons she should not have custody of your daughter.
If you don't know any local lawyer referral sources, use the link below to find a National Association of Counsel for Children member near you who takes parent representation cases.
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You should have had a 72 hour hearing if your child was taken into care. There will be additional hearings - an adjudicatory hearing, dispositional hearing, judicial reviews...and you should request an attorney to assist you through the process. If you have evidence that your Mother is injuring your child, then you should share it with your attorney, so that he or she can help you bring out that information during the proceedings in a procedurally correct way. The State may request that certain evaluations be performed - i.e. they may want you to submit to a parenting assessment, may want your child to undergo a psychological evaluation, etc. Your attorney may request that your mother also submit to an independent psychological evaluation, that an independent guardian ad litem be appointed to represent your child's best interest. The Court may also appoint a child advocate, whose job is to advocate for what your child wants - the child's lawyer. There will be a lot of players and potentially a lot of opinions, and again, it is important to make sure that you are well represented.