Make the first sentence usable
Lead with the reason for writing so the recipient does not have to decode a long emotional introduction. For a message about how to apologize for taking sides in a family conflict, use this factual base: describe what you did, the family context it affected, and any responsibility that still needs attention.
Reduce the work of responding
Offer simple options, a narrow question, or a clear update that can be understood without another conversation. 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.
Respect the boundary already visible
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. A block, explicit refusal, legal restriction, or safety plan takes priority over the desire to explain more.