I don't want my best friends friend staying with us for a weekend
What is it about her that makes you not want her around?
She's been an obtrusive loudmouth when I have wanted to have a few times with my best friend private.
I can understand being irritated at someone with an abrasive personality. You should broach this topic with your best friend with sensitivity; just tell them you want to spend one-on-one time with them and ask them politely to leave their friend at home.
Do you think that will work?
I do. You have every right to only have your best friend stay with you if their friend makes you uncomfortable.