What to do?

What to do with difficult people?  (by this I mean non-believers who are hateful, spiteful or otherwise "difficult" to converse with or be around)

I know the first thing is to pray, which I have been doing with fervor.  But how do you deal with them, I mean day to day, the nitty-gritty stuff. 

I know that we aren't to call non-believers our friends or socialize with them. 2 Corinthians 6:14
Do not be unequally yoked with unbelievers. For what partnership has righteousness with lawlessness? Or what fellowship has light with darkness?
But what about when its a family member? One that you are obligated to take of, not by simple morality but by Timothy 5:8.
But if anyone does not provide for his relatives, and especially for members of his household, he has denied the faith and is worse than an unbeliever. 

I know that I can not know someone's heart, I cannot know if someone is saved.  But God's word tells us we will be able to tell a believer by their works (not to say they are saved by works, they are saved by faith, but works are a fruit of their salvation).

I try to separate all other bad influences from our household.  Most come to us via entertainment but some through people that we no longer cultivate friendships with.  My question is: Am I required by God's law to cultivate a relationship with a person, even though they are not a true Christian (as far as we can tell) and are not what we would consider a good influence for our family IF they are a relative whom we must care for?
Or, are we obligated, as we currently believe, to tend to their earthly needs as best we can while fervently praying for their salvation and God's mercy for their deeds?

This questions sounds simple but then you complicate it with: Do you take this person to church with you? Even though you do not relegate yourself or your family to spending that much time with the person because of their actions any other time?  Is this a point where you "die to self" and take them as a ministry to the lost?  What if they have an alternate place of worship that they may attend (however worldly, useless it may seem)?

Can you sense my exasperation? 

If asked what we feel led to do the choice is clear.  I will be certain that person is cared for, that all of their needs are met.  But do not feel "led" in anyway to have them near my children or self again.  Prayer I believe is our biggest tool in this situation. 

And although I should not care what the outside world thinks of the situation, it worries me that our fellow believers in Christ may see our distancing, our unwillingness to participate in worship with this person (even though their worship is a farce) as a deliberate act of selfishness on our part. 

So, my question is : what to do?