"But they shall fly upon the shoulders of the Philistines toward the west; they shall spoil them of the east together: they shall lay their hand upon Edom and Moab; and the children of Ammon shall obey them." -- (Isaiah 11:14)

Background Reading:
The Obedience of Faith

"they shall lay their hand upon Edom and Moab; and the children of Ammon shall obey them" -- During the Millennial Kingdom, the Lord Jesus Christ will rule from Israel, and all the nations will submit to His authority. If they do not obey Him, they will be punished. The people of Israel at that time will rule over the peoples of the nations that previously oppressed them, as it is written:

For the LORD will have mercy on Jacob, and will yet choose Israel, and set them in their own land: and the strangers shall be joined with them, and they shall cleave to the house of Jacob. And the people shall take them, and bring them to their place: and the house of Israel shall possess them in the land of the LORD for servants and handmaids: and they shall take them captives, whose captives they were; and they shall rule over their oppressors. (Isaiah 14:1-2)

The mention of Edom, Moab, and the children of Ammon in Isaiah 11:14 is similar to a statement in Daniel, chapter 11:

He shall enter also into the glorious land, and many countries shall be overthrown: but these shall escape out of his hand, even Edom, and Moab, and the chief of the children of Ammon. (Daniel 11:41)

The passage in Daniel, chapter 11 does not refer to the time of the Millennial Kingdom, but rather to the time of the Great Tribulation. The Antichrist invades the glorious land (Israel), but Edom, Moab, and the chief of the children of Ammon escape out of the hand of the Antichrist. At the mid-point of the Great Tribulation (3 1/2 years), the Antichrist defiles the temple, at which point the Jews are warned to flee into the mountains:

When ye therefore shall see the abomination of desolation, spoken of by Daniel the prophet, stand in the holy place, (whoso readeth, let him understand:) Then let them which be in Judaea flee into the mountains (Matthew 24:15-16)

In the MacArthur Study Bible, the following note appears for Matt. 24:16:

the mountains. Probably a reference to the region SE of Jerusalem, particularly the Dead Sea area, where there are many caves and places of refuge. David hid from Saul in this area (1 Sam. 23:29). This would also include the hills of Moab and Edom. (MacArthur Study Bible fn. Matt. 24:16)

Thus, during the time of the Great Tribulation, once the Antichrist invades the land of Israel, it is possible that the Jews flee to the land of Moab and Edom and are there protected from the Antichrist. This view is further supported by the account in Revelation, chapter 12:

And the woman fled into the wilderness, where she hath a place prepared of God, that they should feed her there a thousand two hundred and threescore days. (Revelation 12:6)

Here again we see Israel (the woman) flee into the wilderness during the time of the Great Tribulation where the people of Israel are protected from the acts of Satan. The MacArthur Study Bible makes the following comment:

wilderness. God will protect Israel from Satan by hiding her in the wilderness, perhaps in the region of Moab, Ammon, and Edom, east of Palestine. Interestingly, those countries will be specifically spared from the Antichrist's attack against the Holy Land (cf. Dan. 11:41). (MacArthur Study Bible fn. Rev. 12:6)

Thus, the land where perhaps the Jews seek refuge during the time of the Great Tribulation, they will rule over during the time of the Millennial Kingdom.

"The envy also of Ephraim shall depart, and the adversaries of Judah shall be cut off: Ephraim shall not envy Judah, and Judah shall not vex Ephraim." -- (Isaiah 11:13)

Background Reading:
This Thing Is from Me

"Ephraim shall not envy Judah" -- In 1 Kings, chapter 12, we read about the division of the Kingdom of Israel into a northern kingdom (Israel / Ephraim) and a southern kingdom (Judah). The division came about after the death of Solomon. In the future Millennial Kingdom, there will be no division among the tribes of Israel and they will be a united nation once again.

In those days the house of Judah shall walk with the house of Israel, and they shall come together out of the land of the north to the land that I have given for an inheritance unto your fathers. (Jeremiah 3:18)

One of the most descriptive passages about the future unification of Ephraim and Judah appears in Ezekiel, chapter 37:

The word of the LORD came again unto me, saying, Moreover, thou son of man, take thee one stick, and write upon it, For Judah, and for the children of Israel his companions: then take another stick, and write upon it, For Joseph, the stick of Ephraim and for all the house of Israel his companions: And join them one to another into one stick; and they shall become one in thine hand. And when the children of thy people shall speak unto thee, saying, Wilt thou not shew us what thou meanest by these? Say unto them, Thus saith the Lord GOD; Behold, I will take the stick of Joseph, which is in the hand of Ephraim, and the tribes of Israel his fellows, and will put them with him, even with the stick of Judah, and make them one stick, and they shall be one in mine hand. (Ezekiel 37:15-19)

Ezekiel then goes on to state:

And say unto them, Thus saith the Lord GOD; Behold, I will take the children of Israel from among the heathen, whither they be gone, and will gather them on every side, and bring them into their own land: And I will make them one nation in the land upon the mountains of Israel; and one king shall be king to them all: and they shall be no more two nations, neither shall they be divided into two kingdoms any more at all. (Ezekiel 37:21-22)

Thus, once joined during the Millennial Kingdom, Ephraim and Judah will never be divided again. One King shall be King to them all and that King will be the Lord Jesus Christ.