Have them BOTH at the same time!!!!!
Ok seriously then...if you are NOT happy, you really need to reconsider your relationship. Remember (and I say this a lot) If YOU are not happy, you cannot make ANYONE else happy.
You dont have to listen to society either. If you truely like her friend, and think its something worth pursuing, do it. "Thats not right, blah blah blah" ...dont listen to that. But also keep in mind, you can be losing both if it doesnt go well.
And last but not least, your g/f said its ok for you to go out with her? Hmmmm. I have had some girls do crazy things for me, but that IMO just sounds like a trap to me. And sadly, even IF you dont go out with her friend, from here on out she will be wondering what friend of hers you will want next. It will ALWAYS be in the back of her mind. And it will ALWAYS be a negative against you.
I respect your honesty, as I am the same way, but its a catch 22. Tell your girl the truth that they ask for all the time, and its just like the movies "YOU CANT HANDLE THE TRUTH!". Damned if you do damned if you dont.