when i joined (well, upgraded) my AA membership after a breakdown miles from home they took me only so far, and then charged milage on top as it was my first time using them – cost me £500 to get home. since then, every recovery has been free (and there’s been a few!). read the Ts&Cs – you won’t be the first to try it, and I’d be surprised if they’d actually take you to your preferred garage, 50 miles away, for free.
Plus, tbh, this sort of thing is why a membership is, say, £90 and not £50 or whatever. everyone else is paying for this for you.