So faith is the causal agent, and works is an outworking or proof of the faith.
Exactly. Works are not involved in the act of justification before God because justification is based solely upon the acts of Christ in behalf of the "ungodly" only receivd by the "ungodly" by faith (Rom. 4:5).
However, that act of justification is not "without works" as consequences - Eph. 2:10 "created in Christ Jesus UNTO good works." Justification by faith the cause, works the consequences.
james point is where there are no manifest consequences (works) there is no reason to believe their is true faith or spiritual life. He is speaking on a horizontal level between men (vv. 14-16).
Because it is an inheritance, you do not have to qualify by any works to receive it. You qualify as a spiritual descendant of Abraham by having the same faith in the Gospel of Jesus Christ that Abraham had.
Even though Ishmael was the rightful biological (legal) heir,
Here is where I disagree with you. Ishmael was an ILLEGAL heir. God never approved polygamy. He was born out of marriage. The marriage law specifically says the "TWAIN shall be ONE flesh" not the "THREE" or four or five as illustrated by Solomon.
Romans 9 defines the true heirs of the promise in regard to national Israel. Simple physical birth does not qualify any Jew to be the Israel of God. They must be born of flesh and of the Spirit to qualify.