The Church is PART of the Bride of Christ
In Scripture the ‘Church’ is given a definite, direct and defined ‘name’ and that name does NOT originate from any ‘Scriptural allusions’ nor symbolic references.
As such, when we reference the identity of the Church we CANNOT simply pick and choose those allegorical Scriptural Passages that we seem to like best. When we go down the slippery slope of choosing a Church name from ‘symbolic’ rather that direct references than ALL relative symbolism becomes fair play.
For example, the Scriptural allusions of John 3:29, Matt. 9:15; 25:1 & 6 are all references to the Church as the Bride of Christ. These are in NO way direct references but rather ‘allusions’. If we apply this same methodology of allusions in naming the Church then just look what can equally happen.
In Matthew 9:14,15, Jesus referes to his disciples as the ‘Children of the Bridechamber’ and as anyone familiar with Jewish weddings knows the ‘Children of the Bridechamber’ as well as the ‘Bridechamber’ itself refers to the friends of the Bridegroom who are in charge of providing what is necessary for the wedding. (emphasis added)
As such, Jesus was indeed referring to Himself as the Bridegroom that would soon be taken away from them, but He did not call His disciples, who were the beginning nucleus of the New Church, the Bride but rather He called them the ‘Children of the Bridechamber’ or the friends of the Bridegroom.
Again in Matthew 22:2-10 we see that God has made and prepared a ‘wedding’ for His Son Jesus and has called for the Jews to attend that wedding but they made light of it and did NOT come. Therefore, He sent out into the highways (the Gentiles/Church) to furnish ‘ATTENDEES’ to His Son’s wedding. Therefore, here the Church is invited to the wedding of God’s Son but NOT as the Bride of Christ but as ‘Guests of the Bridegroom’.
To this end, as stated before we CANNOT pick and chose a ‘name’ for the Church based on allusive Scriptures. If we do it is just as equitable to say that the Church is a ‘Guest of the Bridegroom’ as to say that the Church is the ‘Bride of Christ’ – this methodology will NOT work.
However, in 2 Cor. 11:2, whereas Apostle makes the allusion ‘I have espoused you to one husband, that I may present you as a chaste virgin to Christ.’, this suggests that Apostle Paul makes it perfectly clear that the Church is ‘married’ to Christ which is also echoed in Romans 7:4. Therefore the Church CAN indeed be 'part' of the Bride of Christ. (emphasis added)
Nonetheless, the summation in many of the above Scriptural Passages (excluding the direct Passage of Romans 7:4) are ‘allusions’ and by NO means can they be used to directly name and identify the Church.
Meanwhile, as I stated at the very beginning there is a direct ‘name’ for the Church in 2 distinct Passages that are NOT allusions and, that name is ‘The Body of Christ’ and NOT the Bride of Christ. (emphasis added)
1 Cor. 12:27
In a brief summary, the Bride of Christ/Lamb's Wife is directly referred to ONLY in Rom. 7:4 and Rev. 21:9-10.
While we may indeed have trouble getting our mortal minds wrapped around the concept revealed above it is nonetheless Scripture and therefore incumbent upon us as believers to figure it out.
The ‘wedding’ analogy throughout Scripture is to represent the ‘Redeemed’ becoming ‘ONE’ with Christ just as a man and wife after marriage become ‘ONE Body’.
Meanwhile, Rev. 21:9-10 reveals that the ‘CITY’ is the Bride of Christ and is populated by the ‘INHABITANTS’ (Church) which is also the Lamb's Wife. As such, it is indeed true that the Church will ‘live’ internally in the City as well as other nations who enter in and out of the glorious light of it.
Although, Rev. 21:11-27 is all about the CITY – with little to no focus on its inhabitants. Look at what it says about the Church dwelling in the Bride.
This chapter is all about the literal CITY New Jerusalem and NOT its inhabitants, they are simply a further description of the events and indwellers that will visit and occupy the CITY.
As stated before, I agree it is extremely difficult to understand the concept of God Christ 'marrying’ a City but that is exactly what Rev. 21:9-10 says. However, we CANNOT approach this with natural human logic because Christ as God is the Bridegroom and the Woman He has chosen to be His 'Wife' is that Holy New City Jerusalem and its inhabitants the Church.
Nonetheless, there is a ‘distinction’ between the City itself and the inhabitants of that City, just as there is a clear distinction between the house you or I are now living in and you or I ourselves – one is not the other, but one dwells within the other.
This is what makes Rev. 21:10-11 so difficult to understand. In terms of a natural wedding, as you have suggested, the Bridegroom goes and builds a House for the Woman and then returns to ‘marry’ her and make her his Bride and Wife and, they go off to live in the House the Bridegroom has built.
However, Rev. 21:10-11 turns this on its natural head – The Bridegroom goes and builds a House and then returns to ‘marry’ the House and make it his Bride and Wife instead of the Woman, whom he however allows to live in the House he has built.
In summary, as stated before we are dealing with the ‘wisdom’ of God here and not the ‘wisdom’ of man.
1 Cor. 2:14