Does saying "God is sufficient for me, and [He is] the best Disposer of affairs" to one's father in a moment of anger necessitate the father's wrath and the resulting disruption of worldly matters, and what is the way to reconciliation?

For a child to argue with their parent when a dispute intensifies is a form of harm and disobedience. Therefore, you must repent for what you have done towards your father. We advise you to seek mediation through some people of goodness. If he does not accept, then increase your prayers for his well-being and ask Allah for soundness. Be keen on honoring him and showing him kindness, for a parent's wrongdoing does not negate the obligation to honor and be kind to them.