What about the Algarve? If you stay in or near Albufeira, you can go to the Old Town in the evenings. There are lots of bars so the kids could sit at a separate table from you, or even in the next bar, and pretend they were 18 but you could keep a close eye on them! I would say the Old Town (and actually the whole of Albufeira) is as safe as you can get. Oh yes, and there are lots of little shops there for them to spend your hard earned cash in and I'm sure they would be happy to join you for a nice meal in one of the many restaurants.
During the day there are any number of fabulous beaches where they can top up their tans, plan what they are going to wear that evening and dream their 14-year old dreams.
They may be too old for kids' things but I bet they'd love Zoomarine and Slide and Splash - and so, I expect, would you. There are jeep safaris into the countryside, where they would have to hang on for dear life, and speedboat trips from the Marina.
The weather will still be hot in September but the town will be less crowded than the high season months - an ideal time to go!