Please, please, please have a conversation with my sister and explain it is enough.
I will tell my sister that I am on-call and the on call rota is set 3 months in advance so if there are any dates I need free, I have to tell them before they set the rota. My sister keeps organising family events, she invites me and gives me 2 weeks notice, as much as I would love to be there, I cannot. When on call I cannot be more than 30 minutes from the office (I do not drive) and she is 45 minutes away by car.
No is never good enough, we go through the same thing every time, get cover, throw a sicky. Of course if its a funeral, christening etc, I will try and get someone to cover but its a nightmare.
When I was working fulltime and doing a fulltime degree course, my dissertation was due and unlike most fulltime students, I didn't get lots of holidays to do assignments and my dissertation, I had to manage my time to the minute...but no, when sister organised an impromptu BBQ and I declined.....NO, was not a complete sentence in her head, it was a negotiation starting point and she would bombard me with guilt trips etc.
I am an adult, no means no, I maybe just as disappointed as you that I can't attend but its just one of those things. If my attendance is so important to you, check I am free before you set the date!