Wow! You certainly have a difficult situation here! Unfortunately, the only way things will ever get better is if you deal with her directly and establish clear boundaries.
I think you absolutely MUST have a conversation with her one-on-one. Start by telling her how important she is to you, and how you truly desire that she has a wonderful relationship with your DD. This part is critical... you want her to be reassured that you're not trying to keep your DD from her, since it sounds like she's (irrationally) afraid of that. For some reason, it seems like grandchildren bring out a lot of insecurities.
Explain that you had really looked forward to this special time alone with your daughter (but keep it brief, you don't want to guilt-trip her). Then, ask her why she did not respect your wishes.
Put the weight on her to explain her actions, not on you to defend yours. She really can't wiggle out of it when you put the ball in her court this way. Don't let her try to manipulate you by pretending it was a misunderstanding. Misunderstandings do happen, but you had made your wishes very clear to her. Absolutely stick to your guns on this fact! Repeat, as many times as necessary, "But I clearly told you that I wanted this time alone with DD." Stick to the facts and do your best to remain calm and assured.
***Try to keep in mind that her actions are of someone who is fearful and insecure, and it might help you deal with her. She might be more fragile than she lets on.***
Depending on your relationship with her, and the way the conversation goes, you may want to let her know that in doing this, it made you feel like she does not respect YOU. But that might be a conversation for a different day. Also, depending on how strong-willed she is, you may need to get her to agree that she will not show up at events unless she is specifically invited.
As others have said, I would end the conversation with some other options for her -- a class she can attend with your daughter, or a regular play date. Do your research ahead of time so that you have a list of solid options. You want her to be a part of your DD's life, but it has to be on YOUR terms. She can't bully her way into it.
As AWFUL as you may feel about having this conversation, you have to do it. Otherwise things will only get worse. You will feel so much better afterwards, even if she is miffed. But if you speak with her respectfully one-on-one, then you've done your part and the responsibility now lies with her to change her ways.
I think it's really important that you do this as soon as possible, before your emotions have had time to fester and you're even angrier. It's so much more effective when you can be calm and collected. Get it out of the way now, and hopefully you'll have to deal with it much less in the future.
Hope that's helpful (can you tell I've dealt with this?)
Bethany
It's a Boy!
William Eric (Wilkes) born 6/16/03