I think this sort of thing has to be taken on a case by case basis. There are, perhaps, times when inviting them over is the best course of action and times when not inviting them over would be.
If the homosexual relative couldn't keep it together during the event and would continually fawn over the "boyfriend" then it would be no, to protect MY family. If I thought that being a Christ-like (to the best of my pathetic ability) witness would serve the relative best, I'd invite him.
In any event, each situation like that would require much prayer.
I agree that it's a case by case thing. If I had a family member who worked for Planned Parenthood or was an abortion "provider," for example, that person would never darken my door.
On the other hand, gay family members who simply appear with a friend and do not do anything improper would probably be welcome; for one thing, perhaps it would keep them in touch with the non-gay world. On the other hand, I would never go to a gay "commitment" ceremony or anything that implied approval, no matter who the family members were.
The same is true of marriages. If a couple is getting married by a JP, they have left the Church anyway. The objective would be to get them back or to make sure that the children, at least, were raised as Catholics until such time as the parents came to their senses. And I would want to remain in contact with them so that I could help this to happen. I'm not sure I'd go to the wedding, but I'd probably send a gift or do something else to stay in touch.
I think it is important to examine each case individually. But it is good to read articles like this because most people don't even think about it. We want our bishops to come down on politicians who support abortion, but we invite a family member who spends her weekends "escorting" girls into abortuaries to spend Easter dinner with us. That's not okay.