In 2nd Corinthians 6:14, it says we are not to associate with unbelievers. Also, in Mathew 19:29 and Mark 10:29-30 it talks about leaving everything for Jesus. Are we to do this even if it means destroying our families?

          The verse you mentioned in 2Cor. 6:14 states;

 "Do not be unequally yoked together with unbelievers. For what fellowship has righteousness with lawlessness? And what communion has light with darkness?"

In this context, Paul is talking to the church of Corinth and telling the people not to be attached to the false Apostles of the church of that time. This chapter of 2nd Corinthians speaks about Paul's concern with the church and their being persuaded by these false Prophets. He encourages them to repent from these sins.

            Unfortunately, there are people and religions that base their beliefs on this verse, to not associate with non-believers and sometimes go to the extreme of divorcing their spouse based on these non-beliefs. However in my opinion, this is not what the verse means.

        In Mathew Ch. 19:29 and Mark 10:29, the verses by both authors are talking about the same thing, and that is leaving everything and receiving a great reward for doing so. Again, in looking at the context of these verses, it is where the disciples after hearing Jesus speak to the rich man, they say to Him;

                                                     "See we have left all and followed you" Mat.19:27

Then in the verses you mentioned, Jesus responds with;

"And everyone who has left house or brothers or sisters or father or mother or wife or children or lands for my name sake shall receive a hundredfold and inherit eternal life." Mat. 19:29

"So Jesus answered and said, "Assuredly, I say to you, there is no one who has left house or brothers or sisters or father or mother or wife or children or lands, for My sake and the gospel's, who shall not receive a hundredfold now in this time-houses and brothers and sisters and mothers and children and lands, with persecutions-and in the age to come, eternal life." Mk. 10:29

In the context of these verses, Jesus is referring specifically to the disciples' decision to follow him. I do not believe this is a justification for us to destroy a home or marriage which is Blessed by God. The family, and marriage is a sacred thing created by God and the Bible gives only two reason acceptable for divorce (infidelity and abandonment of the unbeliever) Yes it is imperative to put Jesus first in our lives, even before your own life and family, but in the correct sense. Every effort should be made to try and minister to a non-believer within a family. It is part of the 'Great commission' we are commanded by Jesus to do.