Anna has been a friend of my parents for 30 years and has been included in many family holidays and when my dad owned his own business, she worked for him for 10 years and I worked with her for 6 of those years. She babysat me frequently as a child and I have babysat for her children. I really adore her and consider her like a favorite aunt.
I think that those calling for Anna's banishment need some perspective. She is threatening to tell embarrassing stories, not engaging in dangerous or reckless behavior. The OP has a good relationship
with her. She will have no relationship
with Anna or seriously damage it, and possibly others, if she blacklists a close family friend from her wedding for what she might say.
If you don't invite Anna to your wedding, the fallout will be far more long-lasting and embarrassing than anything you might endure at your wedding. Afterall, everyone who repeats the story will have to explain why Anna wasn't invited.
The advice to limit the open mic or the toasts are reasonable. You simply cannot control everything that other people will say about you, anyway. You can only control your reaction to it. If she does repeat the stories, you might try, "Oh, that
again," followed by a change of subject. Have a face-to-face talk with her. Ask her as a favor to you, not to repeat those stories.