Make room for the other version
Ask what the other person understood before assuming that you are arguing about the same facts. For a message about how to apologize for forgetting a child's event, use this factual base: describe what you did, the family context it affected, and any responsibility that still needs attention.
Correct the record precisely
Correct only what you can support, acknowledge any real impact, and propose a practical way to prevent repetition. Make a direct repair to the affected person and change the practical pattern that caused the problem. Make the immediate next step clear enough that the recipient can answer without reconstructing the entire history.
Agree on a testable next step
Do not invoke family loyalty, childhood history, or a holiday deadline to force reconciliation. Keep children and vulnerable relatives out of adult conflict and follow any safeguarding or court requirements. Do not recruit an audience, publish private evidence, or turn a misunderstanding into a campaign about character.