YABU for getting upset over this for no reason.
She’s inviting you out for coffee. It’s not a command. Texts can just seem a bit direct sometimes.
If you don’t want to go, just say, “sorry, I can’t tomorrow!”
Or suggest a different date.
You don’t need to feel annoyed about this.
Alternatively, you could say, “I don’t really like it there, it’s a bit noisy, shall we try X instead?”
The ignoring you to talk to the other friend is a different issue. That’s just rude. If she invites both of you, but only talks to one of you, maybe she’s just not a great friend. Only you can decide that, but it sounds as if you don’t like her that much tbh.
Perhaps she feels that she’s the only one who ever makes arrangements and you don’t bother? If you want to stay friends, why don’t you arrange something without the other friend there? “It would be nice to catch up with you one-on-one, shall we go to X at the weekend?”