I hate group texts! I'm not real adept with the ins and outs of using digital devices. Recently I sent a text that I intended for one person, and it went to a group instead. Thank goodness the content was nothing that caused me embarrassment.
I don't think the person who sent you the invitation did anything egregiously bad. She possibly feared she might insult someone by under-inviting. You are perfectly free to decline. She would have zero right to take any offense whatsoever by your opting to miss this event.
I once got a similar invitation to a birthday party. It involved me renting a car and getting a hotel room. I only went because I very much wanted to go. The person throwing the party and the person being celebrated had both done huge favors for me in the past. I was pleased to be invited. I didn't feel the least bit obligated. I just wanted to rekindle our mutual connections. I had a good time.
Had I chosen not to go, I probably would have made some thin pretext of an excuse, like - "I just can't get away on that date, but thanks for thinking of me."
Generally, I don't like to give false excuses to people. My philosophy is that, if I'm telling a lie out of fear, then I'm letting myself be intimidated. Generally, I don't owe anyone an explanation for me doing what I choose to do. However, in the case of a situation like this, I opt for whatever just smoothes out my interaction with the inviting person. I wouldn't make up some big story about some previously planned engagement. That would be me letting myself feel pressured. I'ld just say, "Thanks, but I just can't make it."
One time I got mad at a friend who asked me to do something that would have been a real imposition on me. I gave her a big lecture on how she was asking for too much. When I finished, she responded, "All you had to say was - 'No.'" Well my friend taught me a good lesson. Now I don't get upset when someone makes an inconsiderate request. I just think: "Nice try, friend! Keep dreamin'." Then I might make the flimsiest of excuses, like: "I'ld love to help you out, but I'll be busy taking a nap at that hour." That's my way of saying: "Kiss my behind." People who make outlandish requests often have no shame, so you're not upsetting anyone.