I agree she's doing it for attention. She's getting it too, because there are apparently multiple "adult requests" to stop it.
Remove her from the situation, immediately and firmly, with no discussion or options. If you're at a game, grab her coat with one hand and her hand with your other hand, and take her to the car. If she's a big kid, then you and your husband each take one of her arms and escort her out. If she starts yelling, whichever one of you is able to lift her picks her up and carries her out - yes, just like a toddler having a tantrum. Take her home. Don't give in to nagging or begging in the car. Don't engage in a big debate. Just give her one or two sentences on respect and quote what she said. Then the silent treatment.
When you get home, don't give in. No electronics, no snacks, nothing that she finds fun, just time in her room. When she's done, give her a bunch of chores to do. Next sporting event, she doesn't get to go. Period. No argument. She cannot be respectful of others, she cannot listen to adults, she doesn't get to go out in public.
She goes to school, she goes to church (if you go), and that is it.
You won't make a scene if you take her out of there. You WILL make a scene if you get into an argument with her, debate her behavior, or allow it to continue while everyone reflects on what an ill-mannered child she is.
She gets to go back to fun things if/when she is mature enough to behave.
She's not embarrassing you when she acts out. All kids do that. The embarrassing thing is when it continues and is allowed to continue.
You are right that her friends' parents will not want her around. Neither will the other kids. But that's not the reason you need to get a grip on this. Your main concern should be that she is needy and an attention-grabber who is willing to disrupt other people's fun by misbehaving.
You need more than "some control" - you need complete control. Are kids going to act out or say something inappropriate now and then? Yes. But the continuation and the not responding is a problem. Nip in in the bud now before she is a teenager and it's even harder.
Don't let fear of "what others will think of me and my husband" become the reality - which is that they will think your daughter is running your house instead of you. People will respect your for your immediate response to her, not disrespect you for what she did to provoke it.