"What God has joined together let no man put asunder." Because of this scripture I recently heard someone say that God doesn't join all marriages. Is this true and under what circumstances will He not? (This excludes gay marriage or people remarrying) And if God doesn't join a marriage does that mean the couple is not married in His eyes or that they don't receive the blessings?
The way you took the statement would mean that God is arbitrary in His joining of men and women in marriage. That cannot be. God is impartial (Romans 2:11), He treats all people in the same manner and by the same rules.
You already noted how God would not join all marriages. He clearly would not join in marriage those whose marriage would create a sinful marriage. Therefore, God would not join two homosexuals (I Corinthians 6:9-10), He would not join someone who is already married to another person (Romans 7:2-3), and He would not join someone who left left their spouse for reason other than adultery (Matthew 19:9). Since it is God who does the joining, then it is by God's rules that the marriage takes place and not man's. Men may claim that someone is married, but that doesn't mean God automatically goes along with it.
God states that a marriage is formed by a covenant between the man and woman (Malachi 2:14). Therefore, just because someone moves in with another person, that doesn't make them automatically married. Covenants are special vows that have set features, such as vows exchanged before witnesses, a record of the vows, and a token or witness that the vows exist. See Marriage Covenants.
The point Jesus was making in Matthew 19:6 is that since God defines marriage and does the binding, man does not have the right to override God and declare a marriage ends just because they no longer want to be married. God defines how a marriage starts and He defines how a marriage ends. Man has no say in either matter other than choosing who they wish to marry.
What Jesus is discussing in Matthew 19 has nothing to do with some marriage blessing from God. God has said that finding a good spouse is a blessing (Proverbs 18:22), but there is no passage that states that married couples are given some extra blessing from God.