Wow, that's a bit of a head-wrecker. They need to slow down and think about how hurtful this is for you. I'm not a drama queen and I'm sure you're not either, but this is odd and inconsiderate.
SHE should be trying to meet up with YOU first and anything else is bound to confuse you.
What are you supposed to think now.
I'd have a talk with your brother. MAKE him understand that this is hurtful and confusing. Do NOT pretend to be all cool about it. BEcause I think it is a strange thing for them to arrange. To cut you out of the loop. How else could you feel but hurt!
If your brother goes ahead and meets her, then don't let him off the hook. Let him KNOW that you're surprised and hurt by that decision. Otherwise it'll get more hurtful if they see eachother again and you have to keep pretending you're totally cool with it all.
I find Her behaviour really odd too! Is she not intrigued to meet you? does a biological sister not far out weigh some internet sprite on facebook (no offence to your brother, but you know what I mean here!) Their priorities are questionable.
YOU do not need to get a grip at all. I don't think a human being could react any other way than you have done. Any body would be hurt and confused by this.
I hope that they sort themselves out.