If Jacob, whose name God changed to be called Israel, represents spiritual Israel, Then, according to Jeremiah 2:4, would not spiritual Israel be the ones that were backsliding?
No - Jacob's name was changed, but earthly Israel was given the earthly (but not the spiritual) covenant, and with that covenant, marriage. It is that marriage which God dissolved. God's relationship with spiritual Israel on the other hand, is eternal because it is solely based upon Christ, not man so is the marriage eternal also.
Would you agree that Jacob is one of the elect? Rom 8:33-39, nothing will separate his elect from the love of God.
Yes, I would agree with that.
When the born again elect of God commits a sin we separate ourselves from fellowship with God until we repent. Does God divorce us each time we commit adultery with the world?
No, God does not divorce us, period - that would be impossible. When we are born-again all past spiritual sins are purged through Christ, and future sin not assessed because we are henceforth under grace and not law, so for those born again, it is impossible for them to be guilty of spiritual adultery, especially since adultery is the worship of other gods, which a born-again believer, because they are born-again with the Holy Spirit indwelling them would never do. This is not to say that God does not chastise us when we commit earthly sin or do things that are not God glorifying, because the Bible makes clear that He does so, and that chastisement is most unpleasant and continuing for extremely long time, increasing exponentially with every reoccurrence. It will soon reach a point of diminishing returns where the punishment will greatly outweigh any enjoyment, and so we will stop.
[Heb 1:3 KJV]
3 Who being the brightness of [his] glory, and the express image of his person, and upholding all things by the word of his power, when he had by himself purged our sins, sat down on the right hand of the Majesty on high;
[Heb 12:5-8 KJV]
5 And ye have forgotten the exhortation which speaketh unto you as unto children, My son, despise not thou the chastening of the Lord, nor faint when thou art rebuked of him:
6 For whom the Lord loveth he chasteneth, and scourgeth every son whom he receiveth.
7 If ye endure chastening, God dealeth with you as with sons; for what son is he whom the father chasteneth not?
8 But if ye be without chastisement, whereof all are partakers, then are ye bastards, and not sons.