This is a difficult issue to answer because we can't address all circumstances in which homosexual people could or could not be invited to family events. So, all I can do is speak in generalities and express my opinion.
Let's take a look at different scenarios. Let's say we have a family member who is an atheist and you want to invite him or her over for a birthday party. Does it mean that by doing this you are approving of the person's atheism? It would not.
But then what about inviting a couple who are not married, male and female, to your home for dinner? They stay late, maybe there's a huge snowstorm; and they have to spend the night. Though you don't have the right to tell them what they can and can't do outside of your home, you do have the right to tell them what happens in your home. So, it would be appropriate to say that they are welcome to stay but that you would not agree to them sleeping together. You would, of course, be very polite and state what your moral position is. If they are decent, mature people, they shouldn't have any problem abiding by the rules of your home. So, in this you would not be approving of their fornication, yet you would be helping them out while you have them stay.
Now, what if there were a member of your family who was a homosexual, and he wanted to invite his "partner" with him to your birthday party? Would that be okay? Well, this gets a little more tricky. If the party is for a very young child, I would personally not approve of such an invitation because I would not want to present a bad witness to the children who might be present--and their parents might not approve as well. If, however, it was a birthday party for an adult, then I think that it's up to the individual involved to invite or not invite. Personally, and this again is only my opinion, I would have no problem inviting a homosexual couple into my home for, say, my birthday, because I know that my faith is quite strong; and also I would hope for an opportunity to witness to them. I would, however, state to my hypothetical homosexual relative before their arrival that no overt homosexual activity is to be allowed in the home. This would be the condition. If he did not like that, he would not be invited. After all, I would be free to determine what occurs in my home.
Some Christians are challenged by the presence of homosexuals, and others are not. Some might be repulsed, where others would not be. We want to make sure never to approve of homosexual behavior, but we want to provide an opportunity to witness to them and show them the love of Christ. How this could work out in every situation--well, just can't be determined. But we should try the best we can to present both moral rightness and love to those who are lost.