Write from facts rather than momentum
Pause long enough to remove accusations, assumptions, and details that belong to someone else. For a message about how to apologize for judging a sibling, use this factual base: describe what you did, the family context it affected, and any responsibility that still needs attention.
Offer a proportionate next step
Match the size of the request to the relationship and to what the recipient can reasonably decide now. 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.
Protect privacy on both sides
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. Use the most private legitimate channel available and do not share the exchange to recruit support or pressure.