I'm one of the people who wouldn't think it odd to share a hotel room with a stranger--mostly because this woman isn't a stranger. She's a friend of Betty's whom she hasn't met -yet-.
So I don't think it's so horrible of Betty to want to include both friends. Almost always, I like the friends of my friends. I'm certainly willing to give it a try.
This is where I stand too.
However, there are a couple of "howevers".
First, I'm not Ally.
Second, Even though I agree with the above, I've been in situations of sharing accommodations with people who didn't share my perspective of how vacations should be spent and It can be uncomfortable at best, contentious at worst.
Third, I agree that there are deal breakers for me, main one being I absolutely will not share a room with a smoker.
Betty shouldn't have invited Carly but there's not much Ally can do about that now. It's a fait accompli. What Ally has to do now is figure out her own preference based on the new dynamic. And honestly, even if Betty had, from the start, told Ally, "I'm spending a weekend on the beach with Carly those dates, do you want to come along since you'll be home?" Ally would still be in the same quandary.
So... what is more important to Ally? Seeing Betty, regardless of the circumstances? Or not going on a weekend with someone she doesn't know? Because at this point it seems to be down to those two choices.
My only suggestion for a compromise would be that instead of Ally suggesting Carly join them after the birthday, Ally arranges to join Betty & Carly after the birthday. That way Ally can spend her birthday in town, with other friends or family, and then spend a shorter amount of time with Betty and Carly.