Georgia.
If Department of Family and Children Services fails to remove children from an unstable home, is there anyway you can petition the said county and be able to have the children safely removed? If so, what can you do?
You can report what you know to them and they will investigate. You cannot force them to remove children from a home.
If you are a non-custodial parent and you have a legitimate concern for the safety of the children, you go back to court and petition for custody or to seek some sort of conditions be placed on the custodial parent (drug testing, inspections, counseling, etc.).
Understand that "unstable" does not mean the children are being neglected or abused - at least not to the point that the government has any legitimate purpose in seizing the children. Since "unstable" is a rather subjective term, that would not be sufficient to warrant any government intervention. Perhaps you can articulate something more?