Lol, I tried to edit down your post so I could respond without taking up too much space, but it's really hard to do that without completely losing the sense of what you wrote, so I chopped off some and bolded what I wanted to respond too.
The idea that she has nothing to do is, imo, disrespectful at the very least. I'm sure she has some semblence of a life. It may not seem like much to anyone else, but it means something to her. The invitation/olive branch coming late, even if it was a casual affair, would have been monumental for you both, right? I do think the delay implies... "I don't know if I want to invite her, or really want her to go, but I don't want it to be my fault that she's not there. Now, the ball's in her court and if she doesn't go it's her own fault." How would that make you feel? If it seemed like the olive branch was only sort of extended? If you know she feels alienated and disconnected then it would seem like you would try to change those feelings for her. At least, try not to add to them.
I'm always amazed at how I allow the little things to cause huge chasms in my own extended family. I will bull headedly refuse to yield on something simple and for what? To prove myself bigger or better? When I could just give a little and reap the rewards of a closer, happier relationship. IOW, I do this, so please don't take my 'you need to be more flexible' as 'I am so much better than you.' Rather, see it as one alcoholic saying to another, it's so much easier going an extra block than walking past the ABC, iykwIm.
My responses to invitations are nearly always, I will do my best or I will try. I've had to cancel because of things out of my control so many times that I am downright terrified to accept an invitation without some caveat. I have, literally, missed things I was committed to do, because my home was destroyed. I still have people that see that as a smirch on my character and my word. I said I would be there. Hurricain Isabelle came and devoured my home. I was not there. Therefore, I can't be trusted to be where I said I would. Is it possible that she's had those situations before? She promised to do something, but couldn't and now tries to keep from breaking promises by not making them?
As for timing, at least a week, especially for a celebration.
:iagree: