@YellowMellow99you sound like a lovely, kind and caring Mum, however probably a little bit too soft, (like me)!
I think if it's suspected ADHD/ASD and she already has anxiety then maybe that's why you tend to over compensate for her, and let her get away with quite a lot.
I honestly think that you and your husband have done the right thing by saying that she can't attend, you've already explained your reasons to her why, So just don't engage in any more reactions to her typical teenage stroppy behaviour at not getting what she wants.
My almost 14 year-old sounds very similar to your daughter. She can be incredibly stubborn, can act like a bit of a brat. She does have diagnosed ASD and anxiety and can be quite manipulative but she's also quite insecure and she doesn't like feeling out of control., It's quite difficult having a child with these needs because they're almost like a contradiction and most usual punishments don't tend to work.
I've learnt over the years that you must stay 100% firm, no negotiation when you've said no and you've given a valid reason. You don't need to keep going on giving further punishments for her behaviour because she's choosing to behave like that, just cause she's not getting her way, so don't let it bother you, if she's rude and stroppy and says she doesn't want to talk to you just say "ok" and get on with whatever you were doing.
Reacting and constantly giving punishments or consequences for how she's choosing to react to be told no just prolongs it. Your daughter has every right to feel upset her that she's not going to the activity she really want to go to, but you can't control her reaction to it only the way that you react to her.
sorry for the long winded post, but hopefully it makes some kind of sense
Good luck, it's not easy!