This answer is not intended to provide you with specific legal advice regarding your situation, or to create any attorney-client relationship.
The general rule in Georgia is that the adoptive parent becomes the child's legal parent for all purposes, and that any relationship the adopted child has with regard to the family of the child's biological parent is terminated. Where the adopting parent is a stepparent, the adoption is generally modified so that the biological parent who is married to the adopting stepparent maintains his or her relationship to the children, and only the other original parent is cut off. Since this adoption involved a grandmother adopting her grandchildren, which was likely done for custody purposes rather than with an intent to change the real relationship of the family members, the adoption paperwork should be reviewed, because it may state that the rights of the children to inherit from their biological mother were not to be terminated. However, unless some special provision was made in the adoption order, the children, after the adoption, would normally have ceased to have any inheritance rights with regard to their original mother. Since you mention that the original mother was married at the time of her death and had no other children, her surviving spouse is likely her sole heir, if the adoption did not specifically preserve her children's rights to inherit from her.
The children (or their guardian) may want to have an attorney review the adoption paperwork, to see what, if any, rights they may have.
Normally, adoption severs the parent-child relationship with the biological parent. In that case, the children would not inherit from their biological mother unless she had a will naming them, or if they were named as recipients under a contract, for example a life insurance policy or an investment account with a pay-on-death beneficiary designation.
As my colleague already stated, if the mother had no spouse or other children, her living parents would inherit under typical intestate laws.
With a few more details, a probate attorney versed in the law of the state the mother was living in at the time of her death would be able to answer your question more specifically. The adoption order should be reviewed, as well, to ensure the parent-child relationship was severed.