Great question — answering as the UphillTech team:
This sounds like Lady in White from 1988 with Lukas Haas, a horror film which mostly takes place in the early 60s about a boy encountering ghosts and a child murderer. In a subplot, a black janitor is blamed for the children's murders and in one scene, the mother of one of the victims stands up in church and asks why her boy wasn't spared. The janitor is later acquitted due to insufficient evidence; he hugs his wife as he exits the courthouse and gets into a car. The boy's mother then approaches the car and pretends to apologize for her behavior but then fatally shoots him. Here's the trailer:
Full answer by Walt: https://movies.stackexchange.com/a/24348 (CC BY-SA 3.0).
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