Short answer
They should address disagreements calmly, privately and fairly, seeking reconciliation rather than trying to defeat one another.
Islamic Guidance
What Islam teaches
Islam encourages reconciliation, justice and good conduct. Serious disputes can be addressed with the help of trusted family members or appropriate mediators.
Practical Guidance
What you can consider
Do not share every private disagreement with extended family. If mediation is needed, choose mature and trustworthy people who genuinely seek reconciliation.
Sources
Qur'an 4:35; Qur'an 49:10.