These meetings almost always go over better than expected. When I have a new gf and she’s meeting my family, I make sure it’s some casual event, where there are lots of people and the focus isn’t on her. A BBQ, rather than a sit down dinner. A short family hike, if everyone is into that (not that the family should be short, but the hike should be 😉).
I remember reading an essay about the first meeting of the gf’s family and the bf’s family. The gf’s family was quite wealthy and upper class. The bf’s family was blue collar, working class. To try and make the bf’s family feel comfortable, her father let the air out of one of the car tires. When the bf’s family arrived, he asked the dad to help him change the tire. That broke the ice.
With my past gf’s, I either knew the family because we lived in the same area, or had interacted in a casual way previously. My current gf was different. I had the formal dinner with them. I was just myself. With time they would get to know me, so why fake it in the beginning. I kept in mind that while family acceptance is important, ultimately it’s her acceptance that really matters. I was a bit stressed, but not terribly. Her meeting my family was by bits and pieces, as mostly they didn’t live in this area. It went fine.
I’m sure you’ll do alright. Remember, you’re a guest in their home. It’s their job to make you feel comfortable.
Let us know how it goes, if you feel like sharing that.