@Polly345
I think there are two issues here.
One that both the woman and the girl are labeling you something you do not like. Just tell them to stop. Make it clear it bothers you.
It may be either one is using at as a compliment and may not realize it offends. You need to tell both daughter and mother you are tired of being labelled the crazy one and it needs to stop.
You might say you especially don't want people you are being introduced to, to be familiarized with your friend and her daughter's view of you. (If this is how you feel, which it appears you do - quite rightly in my mind).
Secondly, the friend treats her teenage daughter like an adult. That's tough for you if you don't see her that way, but I doubt this will change.
You've got choices, you probably can't convince the other mum to treat her dd differently but you can choose whether you want to go anywhere with the two of them and meet others with them. Or simply to see your friend, not her daughter.
If the friendship with the mum is important to you, just go out, have coffee, go for drinks with the mum, and explain to her you would like to see her for adult chat and not with her dd.
If she doesn't understand this she sounds a bit dim and you may need to decide whether to continue to see her regularly or wait until her dd grows up a bit and has her own interests.
Good luck.