Being aggressive back and calling her names is bad advice. It's so easy to say 'just beat that bully up!' from the comfort of your own couch isn't it?
From all accounts it seems like shes louder, more confident, more quick witted, and in a way better position than you because if she ever pushes everyone too far she can just fuck off back to her own house and you don't have that luxury. You can't win by rising to her provocations.
My advice would be to make up your mind that she doesn't treat you well enough to be on friendly or 'familial' terms. And you must train yourself to remember that you don't deserve to be treated with such disrespect. Call her out when she interrupts you or makes nasty remarks in front of others. She will probably double down and you'll have to say "well if i'm not getting any respect here than I guess i'm out" and go play videogames, call a real friend, or something. Make yourself happy. The rest of the family are gonna have to start having your back a little better if they want you to have to share the same space with someone who ruins your day.
If she ever tries to escalate things to violence, its time to call the cops.
Don't respond to her if she doesn't address you nicely. Don't do nice things for her just because you're doing them for the nice members of family that you DO like. Show, don't tell, that you only make tea or coffee for people who you respect. Your family will likely treat you like you're being the petty bad guy, and wouldn't it be nice if you bent over backwards so that you could appear to all get along? But it sure feels better to be called 'a bitch' than to be treated like one.
It's ironic that she treats you like a dog when she's the one acting like one, following a feral instinct to enforce a hierarchy by opportunistic behaviour. Just like training a dog, you have to be patient, firm and mature, reward good behaviour and correct bad behaviour.