Having been involved in domestic practice for some time, this sounds more like this ex-husband wants to harass and control his ex-wife and not worry about the safety of the children. Normally 12 and 9 years old are perfectly appropriate ages to be left at home during the day for a 90 minute supermarket trip. Of course, each case is different; if these children are problem kids, have severe special needs or there have been problems in the past, then a certain amount of parental discretion is advised.
However, when an ex-husband threatens "legal actions" over this seeming innocuous situation, I might just chalk it up to a symptom of the bad relationship between mom and dad. If he really felt the kids were in mortal danger, he should have been over there with the police and DFCS. I am assuming that didn't happen.
I'd tell him to go ahead and file something, but if that's all he's got, he'd better prepare to pay for two attorneys - - his and his ex-wife's.
Georgia does not have a set age limit where children can be left alone. However, Georgia does have guidelines regarding when one should leave a child alone without adult supervision. The link I provided explains those guidelines. Much of it depends on the level of the child's maturity. Some 9-year-old children are more adept at supervising themselves for short periods of time than others.