Are Israel and the Church two different kingdoms?

There is only one kingdom because there is only one king.

The kingdom was offered to Israel and not accepted at that time. The kingdom will come and a remnant of Israel will glady receive her king.

Gentiles were being added to the kingdom during the period of Acts. This was a mystery that Paul describes had been hidden.

The end of Mark describes a little of what the kingdom on earth would be like (such as making disciples of all nations).

This kingdom is described briefly in a few places. There will be no more war, people will live longer, nature will be less hostile.

Until the kingdom comes on earth, Christians are like ambassadors of that kingdom in a foreign and hostile country.

Romans 11:12 Now if the fall of them be the riches of the world, and the diminishing of them the riches of the Gentiles; how much more their fulness?

Clearly, there is division in opinion. Not all protestants will agree.

For many protestants, the Kingdom is looked forward to as a literal reign of Chirst on the Earth in the millennium, hence the Millennial reign of Christ. This view holds that the kingdom is only here "in a mystery", such as a seed of the church, and that the outward Kingdom will be here through Israel as chief among the nations, fully healed of her backsliding.

On the other hand, many see the Kingdom as a realm of God, and not aa an outward governmental system. These view the Kingdom as a reign of God to which Israel was offered a part, they rejected, and so, by and large, it went over to the Gentiles.

There are two issues with your question.

First, some disagree that "the church" is the Kingdom. They would say the Kingdom was offered to Israel, they rejected it, and it will come again at His Second Coming. They would claim the church is a parenthesis in the plan of God until it comes back to the Kingdom with Israel. Whatever the church is, they claim, it is unforseen by the Old Covenant, and is not the Kingdom. Not all hold to this, but it is popular.

Second, not all agree that Israel was the Kingdom. In Acts 1:6, the disciples asked Jesus if He would at thay time restore the Kingdom to Israel, indicating that it was not the "Kingdom" at that time.

From these two points, the question of whether the church and Israel are separate kingdoms is probably a "Yes" on the basis that the church and Israel are two separate entities, but "No" from your development of whether God is onlyndealing with the church, and has completely discarded Israel.

From what I can gather of your question, it seems to be 2-fold.

1. Did the church replace Israel in the plan of God?
2. Is the church the Kingdom Jesus talked about?

As to the first, it has become decidedly unpopular in many protestant groups to adhere to "replacement theology", that the church has replaced Israel. Rather, as Paul argues in Romans, Jewish branches were broken off an olive tree, and Gentiles were grafted in, symbolizing the Jews. As such, the "root" of the church, if you will, is still the Jews. Some still hold this replacement position, but it seems without support.

The issue here is tied with the second point. Both agree God is not essentially done with Israel, but the debate is in how God deals with His people.

Those who say the church is not the Kingdom, that it refers to Israel, obviously do not think that God is done with them. They go so far as to say God still deals with them separate, and He will do His own thing with them in its time.

Those who believe, however, that the church represents the Kingdom would hold that Gods heart is still for them, but that they all must be born again in Jesus, that is, become part of the church. This does not, however, mean that God does not regard the nation of Jews as nothing at all. Although there are a variety of opinions, some hold that Pauls words in Romans 10-11 are prophecy concerning their coming salvation. This goes hand in hand with the promises that say that as long as sun and moon, seedtime and harvest, all endure, Israel will be a nation before Him.

This last case seems the most plausible to myself. In the end of Ezekiel 38-39, which details the "Gog-Magog" war, the end result is a regathering of Israel, a nationwide salvation, and God pouring out His Spirit upon the whole nation. As this speaks of the outpouring of thr Spirit, thisncould not have happened before Pentecost, and as Israel waa under judgment, it wouldnt have been between then and 70ad when the Jews were scattered. Likewise, since it speaks of the regathering, it could not have been before 1948, as the Jews were scattered until then. In this regard, it seems, the, although salvation is onky in the church, the church has Jewish roots. And, it appears as though God will indeed have mercy again upon His covenant people, and will see them brought into the salvation which birthed the church.

My answer is from a Seventh Day Adventist perspective, a subset of the protestant view:

The church is not yet the kingdom

In Daniel 2, prophecy depicts a succession of kingdoms, ending with a stone that breaks into pieces all the other kingdoms of the world and rules forever. God's kingdom will not be established until the kingdoms of the world are done away with.

(Dan 2:44) And in the days of these kings the God of heaven will set up a kingdom which shall never be destroyed; and the kingdom shall not be left to other people; it shall break in pieces and consume all these kingdoms, and it shall stand forever.

The church has replaced Israel as 'spiritual Israel'

God's remnant people are those "who keep the commandments of God and have the testimony of Jesus" (Revelation 12:17). Whereas prior to Jesus' first advent, the Jewish nation had the light from God, this ministry has since extended to all who follow Him in faith. There is no partiality shown to those of Jewish decent (Act 10:34-35), we are all spiritually the seed of Abraham.

(Galatians 3:29) And if you are Christ’s, then you are Abraham’s seed, and heirs according to the promise.

(Galatians 3:28) There is neither Jew nor Greek, there is neither slave nor free, there is neither male nor female; for you are all one in Christ Jesus.

Even John the Baptist, when in the spirit, perceived this and said to the multitudes:

(Luke 3:8-9) Therefore bear fruits worthy of repentance, and do not begin to say to yourselves, ‘We have Abraham as our father.’ For I say to you that God is able to raise up children to Abraham from these stones. And even now the ax is laid to the root of the trees. Therefore every tree which does not bear good fruit is cut down and thrown into the fire.”

Finally, Jesus is the true vine and therefore the root. Romans 11 shows that the Gentiles were grafted into this vine and only the unfruitful Jewish followers cut off.

(John 15:1-2) “I am the true vine, and My Father is the vinedresser. Every branch in Me that does not bear fruit He takes away; and every branch that bears fruit He prunes, that it may bear more fruit.