The main objective in dealing with interracial dating conflict is keeping the lines of communication open. This may be the first time you have dated someone outside of your race and it is a new experience for everyone. Think outside of the box and don't fight racist thinking. Instead work on characterizing and emphasizing the amazing attributes of your mate instead of fighting stereotypes.
Be confident in your decisions and remain that way. There is something that attracted you to your mate and do not let external issues affect your relationship with them. You and your mate will deal with many issues during your relationship, with race being only one of those issues. By staying committed to each other, you can avoid some of the issues that many couples face already. You definitely do not need those problems heaped on top of the race issue.
Enlist the help of family and friends that are on your side. The issue may result in the channels of communication becoming blocked. In this case, you can try to circumvent the situation by communicating indirectly through clergy or other family members to keep the lines open. Some types of interracial dating conflicts could have been avoided in other relationships by keeping communication open in some form or another.
Do not resort to name calling. Be the bigger person even though your family member may be acting like a racist or a bigot. It does not help the situation to throw mud and start calling each other ugly names. Turn a deaf ear to what they are saying and move on. You are not going to be able to change the way everyone thinks or feels about interracial dating.
The final tip I have is to realize that no matter what you do, everyone will have some type of opinion about interracial dating. Many people do not believe that the races should mix and you and your mate will come upon situations like this. The best way to handle strangers is to ignore them and move on. Dwelling will not change the way they think and will only make you angry. Let it go and move on. Your relationship will benefit from this type of attitude. It is not worth it to waste time and energy on changing the world when you have interracial dating conflicts closer to home.