Eric,
 
We really need to look into the Catechism for this.
 
Traditionalists tend to promote the idea that the Church completely replaces Israel and that the "Land" promised to Israel has become the Kingdom of God, namely the Church. So, Israel's return to the Land is strictly a call to conversion to the Jews.  But Saint Paul is pretty clear in Romans 9, 10, and 11 that the Promises of God made to Abraham, Isaac, and Jacob, including the physical land, are irrevocable.  So I see this as having a "both-and," not "either-or" understanding.
 
Yes, the Church (including all Christians, to some extent) is part of Israel, but the Land belongs to the 12 Tribes of Israel, the Hebrews, not just the Jews. Jacob had twelve sons, and from each came a tribe. However, Jacob, when blessing Joseph's sons: Manasseh and Ephraim, made them each a tribe unto themselves.  Each tribe was assigned land in the Promised Land, with the exception of Levi. The Levites were the priests, and their portion was the sacrifices offered at the temple. They were also assigned cities within the territories of the other tribes.  So, all these tribes make up Israel or the Hebrews. After Solomon died, the Kingdom of Israel was divided into North and South.

In the North were ten tribes, and it was called Israel.

The Southern Kingdom was called Judah, which was composed mostly of the tribe of Judah, but it also included Benjamin and the Levites living in Jerusalem and other Levite cities found in Judah. 

The Northern Kingdom was invaded by Assyria, and those ten tribes were scattered, never to return until the very last days.  Judah was invaded later by Babylon and was taken into captivity for 70 years. They later returned, and that's when they started referring to them as Jews.  A few stragglers from the Northern Tribes also remained and intermarried with Canaanites and later were called Samaritans. In recent times,  remnants of the lost ten tribes are being found in places like China, India, and so forth. They call themselves Hebrews but don't identify as contemporary Jews because they were never part of the tribe of Judah.

In my opinion, as we continue in the last days, a remnant from each tribe will return to Israel. 

Saint Paul talks of the day when virtually all of the gentiles that will enter the Church will come, at which point God will once again begin to deal with Israel in a more accelerated day.

I personally believe that means we'll see a return of a remnant from each of the other ten tribes to the land of Israel.  Simultaneously, we'll see mass conversions of not just the Jews but people from all the Israelites. The Catechism states that the Second Coming of the Lord is suspended in time, awaiting for Israel to recognize Him. (CCC 674) So that too, is Israel returning to the Land, meaning the Kingdom.   We will also see the rise of the Antichrist. Some Early Church Fathers proposed that the Antichrist would be an Israelite from the Tribe of Dan. But we can't be sure. Many in Israel, indeed the whole world, will believe in him.

As to your other question regarding resources about how or when the Church started to see Herself as the New Israel, I can't really address that in too much detail, as I've not really studied it in debt.  Although as a Protestant Bible Institute student, I took a course called, " the Jewish Roots of Christianity".  The basis of the course was a book called "Our Father Abraham, the Jewish Roots of the Christian Faith." It's written by a professor at Gordon Theological Seminary named Marvin Wilson.  Mind you, it's written from an Evangelical perspective. So, it's a bit skewed. Nevertheless, it's a very good and scholarly work, and it contains a lot of good history. It just must be read critically.  It describes how the Early Church considered itself nothing more than a fulfillment of Judaism. It was a Jewish sect commonly called the Nazarenes.  The Apostles all still worshiped at the Temple.  Later as Gentiles were converted, the Apostles still understood the Church being a fulfillment of Israel. The Gentiles, entering the Church, weren't required to follow the Mosaic Law, but they were being grafted into Israel.  So the idea that the Church is Israel has its roots there. Yes, the Church, again called the Nazarene sect by the Roman Empire and the Jews themselves, was persecuted by some of the Jewish leadership. But in many cases and for periods of time, there was a peaceful coexistence.  This all really started to radically change after the destruction of the Temple, when the Nazarenes refused to fight alongside their fellow Jews against Rome. They remembered the words of Jesus recorded in Matthew 24 and fled to the hills. So there was resentment on the part of Jews that weren't also followers of Christ.  The Nazarenes were thrown out of most of the synagogues.    We can see in the Gospel, according to John, that by the time he wrote, there was huge tension between the Christians or Nazarenes and the Jews. You will see John frequently make pejorative references to the Jews. 

Paul in his later writings, especially Ephesians implies a replacement of sorts in Chapter 3 when he mentions a great mystery of Jews and Gentiles coming together to form one new man.

Later we get an apocryphal epistle attributed to Barnabas. But the Church never declared it was actually written by him. There we begin to read an allegorical reinterpretation of the Mosaic Law, and the author's resentment towards the Jews is thinly veiled.

The final straw that really severed ties between the Church and the Jews, came around 130 A.D., when a man named Simon Bar Kokhba claimed to be Messiah and led yet another military revolt against Rome. The Church, which by now, had a much more defined structure and was absolutely predominantly Gentile by now, wanted no part of this revolt and that sealed it.

That's about as much as I know on the subject. 

I personally believe that it's not an "either-or" situation when we speak of Israel.

The Church is definitely Israel. But that doesn't mean that the Covenant God made with Israel, for that land, has been abrogated. On the contrary, the Covenant is being enforced. Israel was scattered because of her unbelief.  That was a condition of the Covenant. A Covenant is irrevocable. When the terms of the Covenant are broken, the Covenant remains, and the people get broken. So Israel was broken and is under the curse, spelled out clearly in the latter half of Deuteronomy 28. But the curse is for her benefit. And eventually Israel, all the tribes will return to the Land, and that includes both the Land and the Church.

John