I also don’t think your dd’s life sounds particularly nice. Yes, she may have nice things. But by the sound of it, she’s got an emotionally unavailable mum, who flips easily and a severely disabled sibling, who she will undoubtedly see as the favourite child as due to their needs, they get all the energy focused on them.
Having nice stuff is very different from having a nice life. And it sounds as if your dd is permanently walking on egg shells, not knowing when a bomb is going to go off. Ie you. A prepubescent child will try to contain the bomb. Not so a hormonal teen and in this case, it is totally normal that she explodes, creating the bomb. I did it as a teen myself and was punished for it all the time when actually most of the anger was my mother’s stuff. And I get that’s really easily done as I’ve very occasionally fallen into the trap myself of being punitive against my teen dd because of my stuff. And then I’ve had to apologise for messing up. Because when I’ve calmed down, I can see it’s me, not her.
My advice is to talk to your dd. Lean into what you want instead of pushing her away. Tell her you messed up and she then overreacted and you're not going to punish her for swearing at you. However, you want to find a better way of going about all this stuff because you’re both getting really angry and it’s not good for your relationship. And you love her. And want things to be better. And you ask her to work with you on that. Then reassure her you’ll get the bracelet by x deadline, eg Christmas latest even if you have to pay full price.
If otoh, you punish, all you’ll end up doing is creating a terrible dynamic between you and your dd. And you haven’t even entered the trickiest teenage stage, because at 13, she’s only just starting to be at an age, where she really needs you. And girls especially push away from their mums. It’s a natural and normal process and she will probably get meaner before she gets better and you don’t want to be ruining the relationship in the process.
Your dd will soon be spreading her wings and she will need you to be there for her if she’s had too much to drink, taken drugs, if she’s in a very sticky situation with a boy, abusive relationship, if she’s pregnant, miscarrying, been raped and so forth. And if sounds as if you and your dh haven’t yet worked out her to enforce good boundaries to keep your kids safe. Try the book ‘how to talk to teens so teens will listen and listen so teens will talk’. I haven’t read it but the younger kids stuff was great and it’s been recommended on here as a good guide.
I know some people will say what I’m suggesting is so permissive, their parents wouldn’t have put up with that, their parenting didn’t do them any harm etc. The difference being that if you have a good connection with your parents, they can get away with messing up more. And people parented differently in the past to now. And you have already said you and your dd do not have a good connection at the moment.
So I am not suggesting permissive parenting. I’m suggesting firm boundaries and parenting with love. Quite simply, the world has changed. Our kids now expect us to be emotionally intelligent and parent them in an emotionally intelligent way. This is such new territory for most of us because most of our parents won’t have come across emotional intelligence cso we are playing catch up, having to go out and learn it all.
And to your dh: please, never, never punish with food. That’s incredibly dangerous and can lead to life long food issues, even eating disorders and you really don’t want your dd to suffer any of this. Eating disorders are horrendous.