Were the Israelites to treat the Edomites as brothers, or to make war on them?

Israel is not to abhor an Edomite, ‘for he is thy brother’; Edomites may join the congregation in the third generation.

Thou shalt not abhor an Edomite; for he is thy brother: thou shalt not abhor an Egyptian; because thou wast a stranger in his land. The children that are begotten of them shall enter into the congregation of the Lord in their third generation.

Moses asks Edom, as ‘thy brother Israel’, for passage; Edom refuses and comes out armed, and Israel turns away.

And Moses sent messengers from Kadesh unto the king of Edom, Thus saith thy brother Israel, Thou knowest all the travail that hath befallen us: How our fathers went down into Egypt, and we have dwelt in Egypt a long time; and the Egyptians vexed us, and our fathers: And when we cried unto the Lord, he heard our voice, and sent an angel, and hath brought us forth out of Egypt: and, behold, we are in Kadesh, a city in the uttermost of thy border: Let us pass, I pray thee, through thy country: we will not pass through the fields, or through the vineyards, neither will we drink of the water of the wells: we will go by the king’s high way, we will not turn to the right hand nor to the left, until we have passed thy borders. And Edom said unto him, Thou shalt not pass by me, lest I come out against thee with the sword. And the children of Israel said unto him, We will go by the high way: and if I and my cattle drink of thy water, then I will pay for it: I will only, without doing any thing else, go through on my feet. …

Amaziah, who did right ‘yet not like David his father’, defeats Edom in the Valley of Salt and takes Sela.

And he did that which was right in the sight of the Lord, yet not like David his father: he did according to all things as Joash his father did. Howbeit the high places were not taken away: as yet the people did sacrifice and burnt incense on the high places. And it came to pass, as soon as the kingdom was confirmed in his hand, that he slew his servants which had slain the king his father. But the children of the murderers he slew not: according unto that which is written in the book of the law of Moses, wherein the Lord commanded, saying, The fathers shall not be put to death for the children, nor the children be put to death for the fathers; but every man shall be put to death for his own sin. He slew of Edom in the valley of salt ten thousand, and took Selah by war, and called the name of it Joktheel unto this day.

God will judge Edom for its violence against ‘thy brother Jacob’ on the day foreigners entered Jerusalem’s gates.

Shall I not in that day, saith the Lord, even destroy the wise men out of Edom, and understanding out of the mount of Esau? And thy mighty men, O Teman, shall be dismayed, to the end that every one of the mount of Esau may be cut off by slaughter. For thy violence against thy brother Jacob shame shall cover thee, and thou shalt be cut off for ever. In the day that thou stoodest on the other side, in the day that the strangers carried away captive his forces, and foreigners entered into his gates, and cast lots upon Jerusalem, even thou wast as one of them. But thou shouldest not have looked on the day of thy brother in the day that he became a stranger; neither shouldest thou have rejoiced over the children of Judah in the day of their destruction; neither shouldest thou have spoken proudly in the day of distress. Thou shouldest not have entered into the gate of my people in the day of their calamity; yea, thou shouldest not have looked on their affliction in the day of their calamity, nor have laid hands on their substance in the day of their calamity; …