OP, I can understand that safety guidelines dictate to the centimeter that your daughter can still be in a booster seat and that you have an intense desire for her to be safe but, I don't think that this is the hill to die on. (Sorry, poor choice of words cuz I know you're concerned about her safety on the road but, you know what I mean.)
I would have a discussion with her when she's calm and just tell her look, there's a lot of things in life that we don't like, but they're designed for safety. And each one of them have made it to market and are part of our lives today, because people have had to die or be seriously injured before these products were made, and made into law.
That's the terrible thing about safety. You don't realize that it'll save you, until it's too late. If there's an accident, and you're not properly secured, it could change your life. I'm not trying to scare you, I'm just trying to tell you this is why we have to do things we don't always like to do, like why you've been in a booster seat, like why we wear seatbelts, like why we get vaccinations, like why we eat our vegetables!
Absolutely do not give in to her when she's hysterical because she might get the idea that yelling and screaming and crying and carrying on gets results, 100% say that when you can calm down and we can discuss this, that's when we'll talk about it especially if you've already made the decision that she can go without the booster seat, so she'll feel that by having a calm and logical discussion with you, that's "how she won"...
Long after this birthday party has been forgotten, she might remember that having a good logical calm discussion with you and not getting upset got her what she needed to have.
And maybe she'll come to you in the future with other concerns in a common logical way. 9 years old is young but not so young, and kids grow up fast. She'll be a teenager before you realize it. I can only imagine how much anxiety you'll have for her being on the road then when she's a driver.....