I understand you and you don't know how much. Just reading your post my level of anxiety increases.
Ok. The best is to have always a way out in case you can't face the anxiety.
I mean, get ready a good story to quit the appointment. It doesn't mean that you will quit. Go step by step. Only focus on one step each time. For example, get ready to go. When you get this step, focus on the following...that is, reach your frontdoor...always taking in mind that you can give a step back if necessary. And so on.
I normaly when I'm in an appointment, if I feel a lot of anxiety or have a bad moment, I take a while to go to the bathroom or to pretend I have to make a phone call...just to do deep breath exercises.
Think that if they invited you, it's because they like you and want to share with them. I know your firsr fear is to disappoint them. Try to be yourself as much as you can. I know anxiety doesn't help in this point but the more you face to this fear, the more you will be able to get rid of it.