Should I try to reconnect with my family and invite them to my biracial wedding?

It's your call. I personally would because this truly is a special moment. What if you make up and the only thing holding back a relationship between you and your parents is the fact that you didn't invite them. It's not a moment that can be recreated. However, I would make it understood that you won't be standing for any "funny" business at the wedding. This is a formal and respectable event.