Family members who sin publicly

Topic Suggestion/Request:
How do we deal with family members who have sinned publicly?

Reasoning:
I have a cousin who was at one time living in sin with his girlfriend prior to marriage. I confronted him about it several years ago and in response to me confronting him, he basically laughed at me for “foolishly being religious”. At least to my knowledge, he has yet to repent of this sin. Do you have any advice for dealing with such family members? Up until now, I have simply ignored him, but he recently invited me to his daughter’s birthday party. I will not be able to attend the party, but am I obligated to at least respond with gratitude to his invitation? How do I “not fall off the horse” when it comes to not associating with the ungodly vs. a lack of forgiveness for how I was treated? Is this a scenario where I need to “shake the dust from my feet”?