J.,
It's all in the perspective. If this was the 7th grandchild in the family, she wouldn't be doing this. And even if she did, by that time, you'd be immensely grateful for the relief and help if you had several more children to tend to. But if this is the very first grandchild in the family, it means she is so excited to be a grandmother that she can hardly contain herself. Don't weird out on her. She may be a bit of a control freak, and if so, you may need to set some boundaries and rules, but relax and enjoy her enjoying this child as much as you do. If anything ever happened to you, you'd be so glad there was someone else who would watch out for your child as sensitively as you would have. Don't be quick to protect yourself and your imagined 'rights', etc. Where you feel encroached, get practiced at saying,"You're doing it again, grandma!" with a gentle sense of humor and love, but be generous and let her have her time too. You can always send out your own announcements too, whatever you were going to do. Many of the ones she sent may have gone to her/their friends, and not necessarily included your friends away from family setting. You can also set some rules. You can determine what will and won't be done in your house and family, but make no mistake, family counts, because family is there for you when times get hard, and family needs the freedom to celebrate and treasure this child. It's not JUST YOURS, but belongs to "the whole village." Rejoice and be glad, stay positive, state your needs in a positive way, and don't nurse or feed resentment. If she died suddenly, and you had to deal with her loss in your husband's life, the sadness would be as great for you as for him, and then you will have have treasured (and funny) memories to hold about what a crazy, devoted grandma she was. A year from now, when you're harried and can't get everything done, her devotion will be a huge gift. She'll always have your back, because of this child. Nurture that relationship with her. She's not the enemy.
It's all in the perspective. Lighten up ...just a bit, set your boundaries, and then, love on her yourself as much as you can. I lost my beloved father a week ago, and boy, would I trade almost anything to have more time with him!
Congratulations on your precious new soul. He/she belongs to the whole universe in the larger sense. Be glad you have a backup system.