If someone lives in Georgia, and is facing divorce, can the spouse filing for the divorce seek alimony and child support against the business?
I suspect the answer to this would be no. You're not married to the business.
If the business is your spouse's main source of income, or owns the business, then the businesses revenue and his/her income from that business will be considered when calculating child support and alimony.
But because the business is a separate legal entity from your spouse as an individual, you cannot sue the business for child support or alimony.
((Seek the advice of an attorney in your state))