Logically the Kingdom of God can only include Tares (non - elect) if and only if the Church administration and the Kingdom are one and the same. Otherwise the Kingdom of God is soley "seed".
Sorry, but I can't follow your logic here. The overall context of Matthew 13 has been developmental since chapter 5. There is a development of rejection of Christ and John the Baptist by the leadership of Israel, by the cities of Israel and at the conclusion of chapter 13 by his own home town and family. His disicples are witnessing this developmental rejection. This is not rejection by the world but by the professing people of God. Matthew 13 is provided to respond to this obvious problem of rejection by the professed people of God.
Jesus explains this rejection in a series of parables. He explains that this rejection is due to a heart problem with the truth. The first three soils represent different manifest conditions among the professing but lost while the last soil represents the various degrees of productiving among the truly saved. However, the bottom line is this rejected is rooted in a "heart" problem with the truth..
Second, this problem of rejection is more than human rejection but is deeply rooted in a spiritual battle between God and Satan and here he introduces the parable of the tares wiith two explanatory parbles placed between the parable and its explanation.
The realm is "the world" not the church. In the world God's true kingdom is identified as the "seed" that was sowed and sprung up in "the world" not the church. However, Satan has sown "tares" in the same "world" not the church. I was raised in Washington state among wheat fields and I know the difference between wheat and a tare but most people do not because before the harvest they look so much alike that it is almost impossible to distinguish them unless you have a trained eye. At the time of harvest the fruit of the wheat cause the head of grain to bend over while the tares stick straight up.
Now, Jesus says His kingdom is in "the world" (not the church) but in the same "world" Satan has planted counterfits so that to the ordinary eye the the crop growing in "the world" (not the chuch) looks much larger than it really is. That is our "world" (not the church) today. The professing kingdom of God has grown enormous to the ordinary eye. At the end, the angels will be sent to gather out the tares from among the wheat and bind them and burn them and then the true kingdom of God will be made manifest. Meaning, it is not readily manifest now but "hid" (which introduces the parables of hidden treasure and lost treaure in the world - not the church) among the ever growing abundance of tares that dominate the field ("world" not the church).
The two short parables which are not given explanations because they are obvious in their meaning when compared to the overall theme of the parable of the tares follow the primary parable immediately. Both short parables reinforce the main theme of the parable of the tares but provide various distinctons. the primary point of the tares is that the kingdom of God in the world if judged merely by profession is increasing and larger than the true kingdom of beleivers really in the world. This is simply emphasized by the leaven hidden in the dough just as the tares are placed in the field by deceit. Leaven gives the dough an UNNATURAL INCREASE IN SIZE.
The second short parable of the mustard seed illustrates this problem of deception in size. The mustard seed is a very tiny seed but it produces a larger plant than one would expect by looking at the seed. Likewise, when you look at the professing kingdom you see a much larger kingdom than what God actually planted - the size is deception because of the deceiver's deceptive planting of the tares in the same field ("the world") as the true seed where planted.
What does this mean in practical terms to his disicples? You cannot believe everything you hear and see from the professing kingdom because there are hidden problems (1) problems of the heart (2) Satanic counterfits that are at play and this accounts for the developmental rejection they have seen and will continue to see from the professing people of God.
I could go into much greater detail but I have said enough for you to grasp my perspective of these parables.
Therefore, the kingdom is in "the world" but from human perspective it is much larger and filled with confusion because not all who profess have a "heart" for the truth and not all who profess are true believers.
There is no basis that the "field" represents "the church" or that the "kingdom" reprsents the church. The true kingdom is sown all over the "field" or the world. Yet, in ths world there are more than the true kingdom of God that professes to be of God's kingdom. They are the tares. They are found in all churches (Judas) and all denominations, as well, as outside of all institutional churches and denominations.
However, in these parables Jesus provides the key to distinguishing the true from the false wherever we meet them in our life in this "field" or the world. If we do not understand how to distinguish them, then the same impact of rejection may discourage, as well as, lead astray true children of God.