So was it a troop only outing?
Here picnics are for families and siblings are invited to join in games and it's just a big family thing. Especially with something like fireworks afterwards.
Maybe she was confused because you said it was ok to join them for the fireworks.
I'm just thinking of possible misunderstandings.
Either way - if you say No you'd rather not - end of story. She shouldn't challenge you.
I should add - if a friend gave me grief for saying no, I wouldn't consider them a friend. What did you say back?
ETA:
Read your SWH. Thanks.
I didn't get was how a friend goes from being enjoyable and normal - to reacting like this. Usually if people are rude and take advantage, they are like that from the get-go.
I'd just say "I'm not able to" and leave it at that. If they went off on me, I would let them have their minute then I'd say "It's unfortunate you feel that way." Say no more. Like Julie said, if you don't really respond - they get the message.
This woman's problem was not yours to deal with. As Marda says, you're not responsible. So when people say let it go - I agree, you just leave it to her to approach you in the future.