Short answer
Recovery requires calming down, acknowledging mistakes, listening to each other and deciding how the same conflict can be handled differently in the future.
Islamic Guidance
What Islam teaches
Islam encourages reconciliation and appointing mediators when serious marital conflict arises. Forgiveness and good treatment are important qualities in family life.
Practical Guidance
What you can consider
Take time to calm down, apologise where appropriate, avoid publicising private disputes and seek trusted mediation if needed.
Sources
Qur'an 4:35; Qur'an 3:134.