I had a hell of a time introducing my now wife to my Mom. To start off, we met online, and after a few weeks of talking, we decided to meet up. That went fantastically. Meanwhile things at home were getting tense with mom, and after about two months of dating, she and I decided I should move in with her, about an hour and a half away from Mom. Mom promptly had a worry shit-fit. After we got married, it took way too long to get the two to meet. My wife thought Mom was an overly controlling ***** with a self-righteousness complex, and Mom probably thought I'd married a crazy chick. But when they did meet, it was civil enough, but the fact that it was such a trial to meet caused a bit of a rift between my wife and mother. They've gotten better over time though, so there's hope that one day they'll really get along instead of a mutual...slightly better than tolerance.
Dad was a different story. We didn't meet with him until a good while after being married, and we invited him out to dinner. He accepted, came along, and met the wife, me, and her family. That went just fine.
Honestly, if you're an adult, things should be just fine as long as people in your family are somewhat normal. Even if they don't like it, you're a grown up, dammit! You can make your own decisions!